Element contents
Gauge Symmetries, Symmetry Breaking, and Gauge-Invariant Approaches
Published online by Cambridge University Press: 04 July 2023
Summary
Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or whether they can be eliminated. It is also unclear whether they are merely an auxiliary tool to simplify (and possibly localize) calculations or whether they contain independent information. Therefore their status, both in physics and philosophy of physics, remains to be fully clarified. This Element reviews the current state of affairs on both the philosophy and the physics side. In particular, it focuses on the circumstances in which the restriction of gauge theories to gauge invariant information on an observable level is warranted, using the Brout-Englert-Higgs theory as an example of particular current importance. Finally, the authors determine a set of yet to be answered questions to clarify the status of gauge symmetries.
- Type
- Element
- Information
- Online ISBN: 9781009197236Publisher: Cambridge University PressPrint publication: 03 August 2023
References
Afferrante, V., Maas, A., Sondenheimer, R., & Törek, P. (2021). Testing the mechanism of lepton compositeness. SciPost Physics, 10(3), 062. doi: https://doi.org/10.21468/SciPostPhys.10.3.062.Google Scholar
Afferrante, V., Maas, A., & Törek, P. (2020a). Composite massless vector boson. Physical Review D, 101(11), 114506. doi: https://doi.org/10.1103/PhysRevD.101.114506.Google Scholar
Afferrante, V., Maas, A., & Törek, P. (2020b). Toward the spectrum of the SU(2) adjoint Higgs model. Proceedings of Science, ALPS2019, 038. doi: https://doi.org/10.22323/1.360.0038.Google Scholar
Aharonov, Y., & Bohm, D. (1959). Significance of electromagnetic potentials in the quantum theory. The Physical Review, 115(3), 485–491. doi: https://doi.org/10.1103/PhysRev.115.485.Google Scholar
Aharonov, Y., Cohen, E., & Rohrlich, D. (2015). Comment on “Role of potentials in the Aharonov-Bohm effect.” Physical Review A, 92(2), 26101.CrossRefGoogle Scholar
Aharonov, Y., & Rohrlich, D. (2008). Quantum Paradoxes. John Wiley. doi: https://doi.org/10.1002/9783527619115.Google Scholar
Ashtekar, A., & Singh, P. (2011). Loop quantum cosmology: A status report. Classical and Quantum Gravity, 28, 213001. doi: https://doi.org/10.1088/0264-9381/28/21/213001.Google Scholar
Attard, J., & François, J. (2017, Mar.). Tractors and Twistors from conformal Cartan geometry: A gauge theoretic approach II. Twistors. Classical and Quantum Gravity, 34(8), 085004.CrossRefGoogle Scholar
Attard, J., & François, J. (2018). Tractors and Twistors from conformal Cartan geometry: A gauge theoretic approach I. Tractors. Advances in Theoretical and Mathematical Physics, 22(8), 1831–1883.Google Scholar
Attard, J., François, J., Lazzarini, S., & Masson, T. (2018). The dressing field method of gauge symmetry reduction, a review with examples. Pages 377–415 in Kouneiher, J. (Ed.), Foundations of Mathematics and Physics One Century after Hilbert: New Perspectives. Springer.Google Scholar
Babelon, O., & Viallet, C. M. (1979). The geometrical interpretation of the Faddeev-Popov determinant. Physics Letters, 85B, 246–248. doi: https://doi.org/10.1016/0370-2693(79)90589-6.Google Scholar
Baez, J., & Muniain, J. P. (1994). Gauge Fields, Knots and Gravity (Vol. 4). World Scientific Publishing Company.Google Scholar
Bagan, E., Lavelle, M., & McMullan, D. (2000). Charges from dressed matter: Construction. Annals of Physics, 282(2), 471–502.Google Scholar
Banks, T., & Rabinovici, E. (1979, December). Finite-temperature behavior of the lattice abelian Higgs model. Nuclear Physics B, 160(2), 349–379.Google Scholar
Becchi, C. M., & Ridolfi, G. (2006). An Introduction to Relativistic Processes and the Standard Model of Electroweak Interactions. Springer.Google Scholar
Belot, G. (1998, 12). Understanding electromagnetism. The British Journal for the Philosophy of Science, 49(4), 531–555. doi: https://doi.org/10.1093/bjps/49.4.531.Google Scholar
Bertlmann, R. A. (1996). Anomalies in Quantum Field Theory (Vol. 91). Oxford University Press.Google Scholar
Binosi, D., & Papavassiliou, J. (2009). Pinch technique: Theory and applications. Physics Reports, 479, 1–152. doi: https://doi.org/10.1016/j.physrep.2009.05.001.CrossRefGoogle Scholar
Birman, J. L., Nazmitdinov, R. G., & Yukalov, V. I. (2013). Effects of symmetry breaking in finite quantum systems. Physics Reports, 526, 1–91. doi: https://doi.org/10.1016/j.physrep.2012.11.005.Google Scholar
Blagojević, M., Hehl, F. W., & Kibble, T. W. B. (2013). Gauge Theories of Gravitation. Imperial College Press.CrossRefGoogle Scholar
Böhm, M., Denner, A., & Joos, H. (2001). Gauge Theories of the Strong and Electroweak Interaction. Teubner.Google Scholar
Bonora, L., & Cotta-Ramusino, P. (1983). Some remarks on BRS transformations, anomalies and the cohomology of the Lie algebra of the group of gauge transformations. Communications in Mathematical Physics, 87, 589–603.Google Scholar
Brading, K., & Brown, H. (2003). Symmetries and Noether’s theorems. Pages 89–109 in Brading, K. & Castellani, E. (Eds.), Symmetries in Physics: Philosophical Reflections. Cambridge University Press.CrossRefGoogle Scholar
Brading, K., & Brown, H. (2004). Are gauge symmetry transformations observable? The British Journal for the Philosophy of Science, 55(4), 645–665.Google Scholar
Brading, K., & Castellani, E. (Eds.). (2003). Symmetries in Physics: Philosophical Reflections. Cambridge University Press.CrossRefGoogle Scholar
Brans, C., & Dicke, R. H. (1961, Nov). Mach’s principle and a relativistic theory of gravitation. Physical Review, 124(3), 925–935. doi: https://doi.org/10.1103/PhysRev.124.925.Google Scholar
Brown, H. R. (1999). Aspects of objectivity in quantum mechanics. Pages 45–70 in Butterfield, J. & Pagonis, C. (Eds.), From Physics to Philosophy. Cambridge University Press.Google Scholar
Buchmüller, W., Fodor, Z., & Hebecker, A. (1994). Gauge invariant treatment of the electroweak phase transition. Physics Letters B, 331(1), 131–136.Google Scholar
Cap, A., & Slovak, J. (2009). Parabolic Geometries I: Background and General Theory (Vol. 1). American Mathematical Society.Google Scholar
Castellani, E. (2003). On the meaning of symmetry breaking. Pages 321–334 in Brading, K. & Castellani, E. (Eds.), Symmetries in Physics: Philosophical Reflections. Cambridge University Press.Google Scholar
Castellani, E., & Ismael, J. (2016). Which Curie’s principle? Philosophy of Science, 83(5), 1002–1013.Google Scholar
Castellani, E., & Rickles, D. (2017). Introduction to special issue on dualities. Studies in History and Philosophy of Modern Physics, 59, 1–5.CrossRefGoogle Scholar
Catren, G. (2022). On gauge symmetries, indiscernibilities, and groupoid-theoretical equalities. Studies in History and Philosophy of Science, 91, 244–261.Google Scholar
Caudy, W., & Greensite, J. (2008). Ambiguity of spontaneously broken gauge symmetry. Physical Review D, 78(2), 025018.Google Scholar
Chernodub, M. N., Faddeev, L., & Niemi, A. J. (2008). Non-abelian supercurrents and electroweak theory. Journal of High Energy Physics, 12, 014.Google Scholar
Curie, P. (2003). On symmetry in physical phenomena, symmetry of an electric field and of a magnetic field. Pages 311–313 in Brading, K. & Castellani, E. (Eds.), Symmetries in Physics: Philosophical Reflections. Cambridge University Press.Google Scholar
Dasgupta, S. (2022). Symmetry and superfluous structure: A metaphysical overview. Pages 551–562 in Knox, E. & Wilson, A. (Eds.), The Routledge Companion to Philosophy of Physics. Routledge.Google Scholar
De Haro, S., & Butterfield, J. (2021). On symmetry and duality. Synthese, 198, 2973–3013.CrossRefGoogle Scholar
De Haro, S., Teh, N., & Butterfield, J. (2017). Comparing dualities and gauge symmetries. Studies in History and Philosophy of Modern Physics, 59, 68–80.Google Scholar
DeWitt, B. S. (1962). Quantum theory without electromagnetic potentials. Physical Review, 125(6), 2189.CrossRefGoogle Scholar
Dirac, P. A. M. (1955). Gauge-invariant formulation of quantum electrodynamics. Canadian Journal of Physics, 33, 650–660.Google Scholar
Dirac, P. A. M. (1958). The Principles of Quantum Mechanics (4th ed.). Oxford University Press.CrossRefGoogle Scholar
Donnelly, W., & Freidel, L. (2016). Local subsystems in gauge theory and gravity. Journal of High Energy Physics, 2016(9), 102.Google Scholar
Donnelly, W., & Giddings, S. B. (2016). Diffeomorphism-invariant observables and their nonlocal algebra. Physical Review D, 93(2), 024030. ([Erratum: Physical Review D94, no.2, 029903 (2016)]) doi: https://doi.org/10.1103/PhysRevD.93.024030.Google Scholar
Dosch, H. G., & Muller, V. F. (1979). Lattice gauge theory in two space-time dimensions. Fortschritte der Physik, 27, 547. doi: https://doi.org/10.1002/prop.19790271103.Google Scholar
Dudal, D., Peruzzo, G., & Sorella, S. P. (2021). The Abelian Higgs model under a gauge invariant looking glass: Exploiting new Ward identities for gauge invariant operators and the Equivalence Theorem. Journal of High Energy Physics 2021 (2021): n. pag. doi: https://doi.org/10.48550/arXiv.2105.11011.Google Scholar
Dudal, D., van Egmond, D. M., Guimarães, M. S. et al. (2019). Some remarks on the spectral functions of the Abelian Higgs Model. Physical Review D, 100(6), 065009. doi: https://doi.org/10.1103/PhysRevD.100.065009.CrossRefGoogle Scholar
Dudal, D., van Egmond, D. M., Guimarães, M. S. et al. (2020). Gauge-invariant spectral description of the Higgs model from local composite operators. JHEP, 02, 188. doi: https://doi.org/10.1007/JHEP02(2020)188.Google Scholar
Dudal, D., van Egmond, D. M., Guimarães, M. S. et al. (2021). Spectral properties of local gauge invariant composite operators in the Yang–Mills–Higgs model. European Physical Journal C, 81(3), 222. doi: https://doi.org/10.1140/epjc/s10052-021-09008-9.Google Scholar
Earman, J. (1989). World Enough and Space-Time: Absolute versus Relational Theories of Space and Time. The Massachusetts Institute of Technology Press.Google Scholar
Earman, J. (2002). Symmetry, empirical equivalence, and identity. Philosophy of Science, 69, 209–220.CrossRefGoogle Scholar
Earman, J. (2004a). Curie’s principle and spontaneous symmetry breaking. International Studies in Philosophy of Science, 18, 173–198.Google Scholar
Earman, J. (2004b). Laws, symmetry, and symmetry breaking: Invariance, conservation principles, and objectivity. Philosophy of Science, 71, 1227–1241.Google Scholar
Egger, L., Maas, A., & Sondenheimer, R. (2017). Pair production processes and flavor in gauge-invariant perturbation theory. Modern Physics Letters A, 32(38), 1750212. doi: https://doi.org/10.1142/S0217732317502121.Google Scholar
Ehrenberg, W., & Siday, R. E. (1949). The refractive index in electron optics and the principles of dynamics. Proceedings of the Physical Society. Section B, 62(1), 8–21. doi: https://doi.org/10.1088/0370-1301/62/1/303.Google Scholar
Elitzur, S. (1975). Impossibility of spontaneously breaking local symmetries. Physical Review D, 12(12), 3978–3982.CrossRefGoogle Scholar
Evertz, H. G., Jersak, J., Lang, C. B., & Neuhaus, T. (1986). SU(2) Higgs boson and vector boson masses on the lattice. Physics Letters, B171, 271. doi: https://doi.org/10.1016/0370-2693(86)91547-9.Google Scholar
Eynck, T., Lyre, H., & Rummell, N. (2001). A versus B! topological nonseparability and the Aharonov–Bohm effect. Contribution for the International IQSA Conference: Quantum Structure V. Archive preprint: http://philsci-archive.pitt.edu/404/.Google Scholar
Faddeev, L. D. (2009). An alternative interpretation of the Weinberg-Salam model. In Begun, V., Jenkovszky, L. L., & Polański, A. (Eds.), Progress in High Energy Physics and Nuclear Safety (pp. 3–8). Springer.Google Scholar
Fernandez, R., Fröhlich, J., & Sokal, A. (1992). Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory. Springer.Google Scholar
Fernbach, S., Lechner, L., Maas, A., Plätzer, S., & Schöfbeck, R. (2020). Constraining the Higgs boson valence contribution in the proton. Physical Review D, 101(11), 114018. doi: https://doi.org/10.1103/PhysRevD.101.114018.Google Scholar
Fournel, C., François, J., Lazzarini, S., & Masson, T. (2014). Gauge invariant composite fields out of connections, with examples. International Journal of Geometric Methods in Modern Physics, 11(1), 1450016.Google Scholar
Fradkin, E. H., & Shenker, S. H. (1979). Phase diagrams of lattice gauge theories with Higgs fields. Physical Review D, 19, 3682–3697. doi: https://doi.org/10.1103/PhysRevD.19.3682.Google Scholar
François, J. (2014). Reduction of Gauge Symmetries: A New Geometrical Approach. Thesis. Aix-Marseille Université.Google Scholar
François, J. (2019). Artificial versus substantial gauge symmetries: A criterion and an application to the electroweak model. Philosophy of Science, 86(3), 472–496.CrossRefGoogle Scholar
François, J. (2021a). Differential geometry of gauge theory: An introduction. In Proceedings of XVI Modave Summer School in Mathematical Physics (Modave 2020). Proceedings of Science, vol. 389. doi: https://doi.org/10.22323/1.389.0002.Google Scholar
François, J. (2021b). Bundle geometry of the connection space, covariant Hamiltonian formalism, the problem of boundaries in gauge theories, and the dressing field method. Journal of High Energy Physics, 03, 225.CrossRefGoogle Scholar
François, J., Lazzarini, S., & Masson, T. (2015, Feb). Nucleon spin decomposition and differential geometry. Physical Review D, 91, 045014.Google Scholar
François, J., Parrini, N., & Boulanger, N. (2021). Note on the bundle geometry of field space, variational connections, the dressing field method, & presymplectic structures of gauge theories over bounded regions. Journal of High Energy Physics, 12, 186.CrossRefGoogle Scholar
Freedman, D. Z., & Van Proeyen, A. (2012). Supergravity. Cambridge University Press.CrossRefGoogle Scholar
Freidel, L., & Teh, N. (2022). Substantive general covariance and the Einstein–Klein dispute: A Noetherian approach. Pages 274–295 in Read, J. & Teh, N. (Eds.), The Philosophy and Physics of Noether’s Theorems. Cambridge University Press.Google Scholar
Friederich, S. (2013). Gauge symmetry breaking in gauge theories: In search of clarification. European Journal for Philosophy of Science, 3(2), 157–182.Google Scholar
Friederich, S. (2014). A philosophical look at the Higgs mechanism. Journal for General Philosophy of Science, 45, 335–350.Google Scholar
Friederich, S. (2015). Symmetry, empirical equivalence, and identity. The British Journal for the Philosophy of Science, 66(3), 537–559.Google Scholar
Friederich, S. (2017). EPSA15 selected papers. Pages 153–165 in Massimi, M., Romeijn, J.-W., & Schurz, G. (Eds.), Symmetries and the Identity of Physical States. Springer.Google Scholar
Frisch, M. (2005). Inconsistency, Asymmetry, and Non-locality: A Philosophical Investigation of Classical Electrodynamics. Oxford University Press.CrossRefGoogle Scholar
Fröhlich, J., Morchio, G., & Strocchi, F. (1980). Higgs phenomenon without a symmetry breaking order parameter. Physics Letters B, 97, 249. doi: https://doi.org/10.1016/0370-2693(80)90594-8.Google Scholar
Fröhlich, J., Morchio, G., & Strocchi, F. (1981). Higgs phenomenon without a symmetry breaking order parameter. Nuclear Physics B, 190, 553–582. doi: https://doi.org/10.1016/0550-3213(81)90448-X.CrossRefGoogle Scholar
Garajeu, D., Grimm, R., & Lazzarini, S. (1995). W-gauge structures and their anomalies: An algebraic approach. Journal of Mathematical Physics, 36, 7043–7072.Google Scholar
Geiller, M. (2017). Edge modes and corner ambiguities in 3D Chern–Simons theory and gravity. Nuclear Physics B, 924, 312–365.Google Scholar
Giddings, S., & Weinberg, S. (2019). Gauge-invariant observables in gravity and electromagnetism: Black hole backgrounds and null dressings. doi: https://doi.org/10.48550/arXiv.1911.09115.Google Scholar
Gomes, H. (2019a). Gauging the boundary in field-space. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 67, 89–110.Google Scholar
Gomes, H. (2019b). Noether charges, gauge-invariance, and non-locality. Pages 296–321 in Read, J. & Teh, N. (Eds.), The Philosophy and Physics of Noether’s Theorems: A Centenary Volume. Cambridge University Press. doi: https://doi.org/10.1017/9781108665445.013.Google Scholar
Gomes, H. (2021). Holism as the empirical significance of symmetries. European Journal for the Philosophy of Science, 67, 89–110.Google Scholar
Gomes, H., Hopfmüller, F., & Riello, A. (2019). A unified geometric framework for boundary charges and dressings: Non-abelian theory and matter. Nuclear Physics B, 941, 249–315.Google Scholar
Gomes, H., & Riello, A. (2017). The observer’s ghost: Notes on a field space connection. Journal of High Energy Physics, 05, 017. doi: https://doi.org/10.1007/JHEP05(2017)017.Google Scholar
Gomes, H., & Riello, A. (2018). Unified geometric framework for boundary charges and particle dressings. Physical Review D, 98, 025013.Google Scholar
Gomes, H., & Riello, A. (2021). The quasilocal degrees of freedom of Yang–Mills theory. SciPost Physics, 10, 130. doi: https://doi.org/10.21468/SciPostPhys.10.6.130.Google Scholar
Gomes, H., Roberts, B., & Butterfield, J. (2021). The gauge argument: A Noether reason. doi: https://doi.org/10.48550/arXiv.2105.11154.Google Scholar
Grassi, P. A., Kniehl, B. A., & Sirlin, A. (2002). Width and partial widths of unstable particles in the light of the Nielsen identities. Physical Review D, 65, 085001. doi: https://doi.org/10.1103/PhysRevD.65.085001.Google Scholar
Greaves, H., & Wallace, D. (2014). Empirical consequences of symmetries. The British Journal for the Philosophy of Science, 65, 59–89.Google Scholar
Greensite, J., & Matsuyama, K. (2017). A confinement criterion for gauge theories with matter fields. Physical Review, D 96(9), 094510. doi: https://doi.org/10.1103/PhysRevD.96.094510.Google Scholar
Greensite, J., & Matsuyama, K. (2018). What symmetry is actually broken in the Higgs phase of a gauge-Higgs theory? Physical Review, D 98(7), 074504. doi: https://doi.org/10.1103/PhysRevD.98.074504.Google Scholar
Gribov, V. N. (1978). Quantization of non-abelian gauge theories. Nuclear Physics B, 139, 1–19.Google Scholar
Grosse-Knetter, C., & Kögerler, R. (1993). Unitary gauge, Stueckelberg formalism, and gauge-invariant models for effective Lagrangians. Physical Review D, 48, 2865–2876.Google Scholar
Haag, R. (1992). Local Quantum Physics: Fields, Particles, Algebras. Texts and Monographs in Physics. Springer.Google Scholar
Hamilton, M. J. D. (2017). Mathematical Gauge Theory: With Applications to the Standard Model of Particle Physics (Vol. 1st edition). Springer.Google Scholar
Healey, R. (1997). Nonlocality and the Aharonov–Bohm effect. Philosophy of Science, 64(1), 18–41. doi: https://doi.org/10.1086/392534.Google Scholar
Healey, R. (1999). Quantum analogies: A reply to Maudlin. Philosophy of Science, 66(3), 440–447.Google Scholar
Healey, R. (2009). Perfect symmetries. The British Journal for the Philosophy of Science, 60, 697–720.Google Scholar
Hehl, F. W., McCrea, J. D., Mielke, E. W., & Ne’eman, Y. (1995). Metric-affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance. Physics Reports, 258(1–2), 1–171. doi: https://doi.org/10.1016/0370-1573(94)00111-F.Google Scholar
Hehl, F. W., Von Der Heyde, P., Kerlick, G. D., & Nester, J. M. (1976). General relativity with spin and torsion: Foundations and prospects. Reviews of Modern Physics, 48, 393–416. doi: https://doi.org/10.1103/RevModPhys.48.393.Google Scholar
Heinzl, T., Ilderton, A., Langfeld, K., Lavelle, M., & McMullan, D. (2008). The ice-limit of Coulomb gauge Yang–Mills theory. Physical Review D, 78, 074511. doi: https://doi.org/10.1103/PhysRevD.78.074511.Google Scholar
Hetzroni, G. (2020). Relativity and equivalence in Hilbert space: A principle theory approach to the Aharonov–Bohm effect. Foundations of Physics, 50, 120–135. doi: https://doi.org/10.1007/s10701-020-00322-y.Google Scholar
Hetzroni, G. (2021). Gauge and ghosts. The British Journal for the Philosophy of Science, 72(3), 773–796. doi: https://doi.org/10.1093/bjps/axz021.Google Scholar
Hetzroni, G., & Stemeroff, N. (2023). Mathematical analogies in physics: The curious case of gauge symmetries. In Posy, C. & Ben-Menahem, Y. (Eds.), Mathematical Knowledge, Objects and Applications. Springer. (Forthcoming)Google Scholar
Higgs, P. W. (1966, May). Spontaneous symmetry breakdown without massless bosons. Physical Review, 145, 1156–1163.Google Scholar
Hiley, B. (2013). The early history of the Aharonov–Bohm effect. arXiv preprint arXiv:1304.4736.Google Scholar
Ilderton, A., Lavelle, M., & McMullan, D. (2010). Symmetry breaking, conformal geometry and gauge invariance. Journal of Physics A: Mathematical and Theoretical, 43(31), 312002.Google Scholar
Irges, N., & Koutroulis, F. (2017). Renormalization of the Abelian–Higgs model in the and Unitary gauges and the physicality of its scalar potential. Nuclear Physics B, 924, 178–278.Google Scholar
Ismael, J. (2022). Symmetry and superfluous structure: Lessons from history and tempered enthusiasm. In Knox, E. & Wilson, A. (Eds.), The Routledge Companion to Philosophy of Physics. Routledge.Google Scholar
Kibble, T. W. (2015). History of electroweak symmetry breaking. Journal of Physics: Conference Series, 626(1). doi: https://doi.org/10.1088/1742-6596/626/1/012001.Google Scholar
Kibble, T. W. B. (1967). Symmetry breaking in non-abelian gauge theories. Physical Review, 155, 1554–1561.Google Scholar
Kogut, J. B. (1979). An introduction to lattice gauge theory and spin systems. Reviews of Modern Physics, 51, 659. doi: https://doi.org/10.1103/RevModPhys.51.659.Google Scholar
Kondo, K.- I. (2018). Gauge-independent Brout–Englert–Higgs mechanism and Yang–Mills theory with a gauge-invariant gluon mass term. European Physical Journal, C78(7), 577. doi: https://doi.org/10.1140/epjc/s10052-018-6051-2.Google Scholar
Kosmann-Schwarzbach, Y. (2022). The Noether theorems in context. Pages 4–24 in Read, J. & Teh, N. (Eds.), The Philosophy and Physics of Noether’s Theorems. Cambridge University Press.Google Scholar
Kosmann-Schwarzbach, Y., & Schwarzbach, B. E. (2011). The Noether Theorems: Invariance and Conservation Laws in the Twentieth Century (Vol. 1st edition). Springer.Google Scholar
Kosso, P. (2000). The empirical status of symmetries in physics. The British Journal for the Philosophy of Science, 51, 81–98.Google Scholar
Lavelle, M., & McMullan, D. (1995). Observables and gauge fixing in spontaneously broken gauge theories. Physics Letters B, 347(1), 89–94.Google Scholar
Lavelle, M., & McMullan, D. (1997). Constituent quarks from QCD. Physics Reports, 279, 1–65.Google Scholar
Leader, E., & Lorcé, C. (2014). The angular momentum controversy: What is it all about and does it matter? Physics Reports, 514, 163–248.Google Scholar
Lee, B., & Zinn-Justin, J. (1972). Spontaneously broken gauge symmetries II: Perturbation theory and renormalization. Physical Review D, 5, 3137–3155. doi: https://doi.org/10.1103/PhysRevD.5.3137,10.1103/PhysRevD.8.4654.Google Scholar
Lee, I.- H., & Shigemitsu, J. (1986). Spectrum calculations in the lattice Georgi–Glashow model. Nuclear Physics B, 263, 280–294. doi: https://doi.org/10.1016/0550-3213(86)90117-3.Google Scholar
London, F. (1927). Quantenmechanische Deutung der Theorie von Weyl. Zeitschrift für Physik A: Hadrons and Nuclei, 42, 375.Google Scholar
Lorcé, C. (2013). Geometrical approach to the proton spin decomposition. Physical Review D, 87, 034031.Google Scholar
Lyre, H. (2000). A generalized equivalence principle. International Journal of Modern Physics D, 9(06), 633–647.Google Scholar
Lyre, H. (2003). On the Equivalence of Phase and Field Charges. (arXiv preprint: hep-th/0303259)Google Scholar
Lyre, H. (2004). Lokale Symmetrien und Wirklichkeit : Eine naturphilosophische Studie über Eichtheorien und Strukturenrealismus. Mentis.Google Scholar
Lyre, H. (2008). Does the Higgs mechanism exist? International Studies in the Philosophy of Science, 22(2), 119–133.Google Scholar
Maas, A. (2013). Describing gauge bosons at zero and finite temperature. Physics Reports, 524, 203. doi: https://doi.org/10.1016/j.physrep.2012.11.002.CrossRefGoogle Scholar
Maas, A. (2019). Brout–Englert–Higgs physics: From foundations to phenomenology. Progress in Particle and Nuclear Physics, 106, 132–209. doi: https://doi.org/10.1016/j.ppnp.2019.02.003.Google Scholar
Maas, A. (2020). The Fröhlich–Morchio–Strocchi mechanism and quantum gravity. SciPost Physics, 8(51), 1–18.Google Scholar
Maas, A., & Mufti, T. (2014). Two- and three-point functions in Landau gauge Yang–Mills–Higgs theory. Journal of High Energy Physics, 04, 006. doi: https://doi.org/10.1007/JHEP04(2014)006.Google Scholar
Maas, A., & Mufti, T. (2015). Spectroscopic analysis of the phase diagram of Yang–Mills–Higgs theory. Physical Review D, 91(11), 113011. doi: https://doi.org/10.1103/PhysRevD.91.113011.Google Scholar
Maas, A., & Pedro, L. (2016). Gauge invariance and the physical spectrum in the two-Higgs-doublet model. Physical Review D, 93(5), 056005. doi: https://doi.org/10.1103/PhysRevD.93.056005.Google Scholar
Maas, A., Raubitzek, S., & Törek, P. (2019). Exploratory study of the off-shell properties of the weak vector bosons. Physical Review D, 99(7), 074509. doi: https://doi.org/10.1103/PhysRevD.99.074509.Google Scholar
Maas, A., & Sondenheimer, R. (2020). Gauge-invariant description of the Higgs resonance and its phenomenological implications. Physical Review D, 102, 113001. doi: https://doi.org/10.1103/PhysRevD.102.113001.Google Scholar
Maas, A., Sondenheimer, R., & Törek, P. (2019). On the observable spectrum of theories with a Brout–Englert–Higgs effect. Annals of Physics, 402, 18–44. doi: https://doi.org/10.1016/j.aop.2019.01.010.Google Scholar
Maas, A., & Törek, P. (2017). Predicting the singlet vector channel in a partially broken gauge-Higgs theory. Physical Review D, 95(1), 014501. doi: https://doi.org/10.1103/PhysRevD.95.014501.Google Scholar
Maas, A., & Törek, P. (2018). The spectrum of an SU(3) gauge theory with a fundamental Higgs field. Annals of Physics, 397, 303–335. doi: https://doi.org/10.1016/j.aop.2018.08.018.CrossRefGoogle Scholar
Maas, A., & Zwanziger, D. (2014). Analytic and numerical study of the free energy in gauge theory. Physical Review D, 89, 034011. doi: https://doi.org/10.1103/PhysRevD.89.034011.Google Scholar
Mack, G. (1981). Physical principles, geometrical aspects, and locality properties of gauge field theories. Fortschritte der Physik, 29(4), 135–185. doi: https://doi.org/10.1002/prop.19810290402.Google Scholar
Mainland, G., & O’Raifeartaigh, L. (1975). Point transformation and renormalization in the unitary gauge for nonabelian fields. Physical Review D, 12, 489.Google Scholar
Mañes, J., Stora, R., & Zumino, B. (1985). Algebraic study of chiral anomalies. Communications in Mathematical Physics, 102, 157–174.Google Scholar
Martin, C. A. (2003). On continuous symmetries and the foundations of modern physics. In Brading, K. & Castellani, E. (Eds.), Symmetries in Physics: Philosophical Reflections. Cambridge University Press.Google Scholar
Masson, T., & Wallet, J. C. (2011). A remark on the Spontaneous Symmetry Breaking Mechanism in the Standard Model. arXiv:1001.1176.Google Scholar
Mathieu, P., Murray, L., Schenkel, A., & Teh, N. J. (2020). Homological perspective on edge modes in linear Yang–Mills and Chern–Simons theory. Letters in Mathematical Physics, 110(7), 1559–1584.Google Scholar
Maudlin, T. (1998). Discussion: Healey on the Aharonov–Bohm effect. Philosophy of Science, 65(2), 361–368.Google Scholar
Mills, R. (1989). Gauge fields. American Journal of Physics, 57(6), 493–507. doi: https://doi.org/10.1119/1.15984.Google Scholar
Montvay, I., & Münster, G. (1994). Quantum Fields on a Lattice. (Cambridge Monographs on Mathematical Physics). Cambridge University Press.Google Scholar
Morris, T. R. (2000a). A gauge invariant exact renormalization group. 1. Nuclear Physics B, 573, 97–126. doi: https://doi.org/10.1016/S0550-3213(99)00821-4.Google Scholar
Morris, T. R. (2000b). A gauge invariant exact renormalization group. 2. Journal of High Energy Physics, 12, 012. doi: https://doi.org/10.1088/1126-6708/2000/12/012.Google Scholar
Mottola, E. (1995). Functional integration over geometries. Journal of Mathematical Physics, 36(5), 2470–2511. doi: https://doi.org/10.1063/1.531359.Google Scholar
Murgueitio Ramírez, S. (2021). A puzzle concerning local symmetries and their empirical significance. The British Journal for the Philosophy of Science.Google Scholar
Murgueitio Ramírez, S., & Teh, N. (2020). Abandoning Galileo’s Ship: The quest for non-relational empirical significance. The British Journal for the Philosophy of Science.Google Scholar
Nielsen, N. K. (1975). On the gauge dependence of spontaneous symmetry breaking in gauge theories. Nuclear Physics B, 101, 173–188. doi: https://doi.org/10.1016/0550-3213(75)90301-6.Google Scholar
Norton, J. D. (1993). General covariance and the foundations of general relativity: Eight decades of dispute. Reports on Progress in Physics, 56(7), 791–858. doi: https://doi.org/10.1088/0034-4885/56/7/001.Google Scholar
Norton, J. D. (2003). General covariance, gauge theories, and the Kretschmann objection. In Brading, K. & Castellani, E. (Eds.), Symmetries in Physics: Philosophical Reflections (pp. 110–123). Cambridge University Press. doi: https://doi.org/10.1017/cbo9780511535369.007.Google Scholar
Nounou, A. M. (2003). A fourth way to the Aharonov–Bohm effect. In Brading, K. & Castellani, E. (Eds.), Symmetries in Physics: Philosophical Reflections. Cambridge University Press.Google Scholar
Osterwalder, K., & Seiler, E. (1978). Gauge field theories on the lattice. Annals of Physics, 110, 440. doi: https://doi.org/10.1016/0003-4916(78)90039-8.Google Scholar
Papavassiliou, J., & Pilaftsis, A. (1995). Gauge invariance and unstable particles. Physical Review Letters, 75, 3060–3063. doi: https://doi.org/10.1103/PhysRevLett.75.3060.Google Scholar
Papavassiliou, J., & Pilaftsis, A. (1996a). A gauge independent approach to resonant transition amplitudes. Physical Review D, 53, 2128–2149. doi: https://doi.org/10.1103/PhysRevD.53.2128.Google Scholar
Papavassiliou, J., & Pilaftsis, A. (1996b). Gauge invariant resummation formalism for two point correlation functions. Physical Review D, 54, 5315–5335. doi: https://doi.org/10.1103/PhysRevD.54.5315.Google Scholar
Papavassiliou, J., & Pilaftsis, A. (1998). Gauge and renormalization group invariant formulation of the Higgs boson resonance. Physical Review D, 58, 053002. doi: https://doi.org/10.1103/PhysRevD.58.053002.Google Scholar
Pauli, W. (1941). Relativistic field theories of elementary particles. Reviews of Modern Physics, 13(3), 203–232. doi: https://doi.org/10.1103/RevModPhys.13.203.Google Scholar
Philipsen, O., Teper, M., & Wittig, H. (1996). On the mass spectrum of the SU(2) Higgs model in - dimensions. Nuclear Physics B, 469, 445–472. doi: https://doi.org/10.1016/0550-3213(96)00156-3.Google Scholar
Pitts, J. B. (2008). General covariance, artificial gauge freedom and empirical equivalence. Unpublished doctoral dissertation. Graduate School of the University of Notre Dame.Google Scholar
Pitts, J. B. (2009). Empirical equivalence, artificial gauge freedom and a generalized Kretschmann objection. https://arxiv.org/abs/0911.5400.Google Scholar
Pitts, J. B. (2012). The nontriviality of trivial general covariance: How electrons restrict time coordinates, spinors (almost) fit into tensor calculus. Studies in History and Philosophy of Modern Physics, 43, 1–24.Google Scholar
Pooley, O. (2017). Background independence, diffeomorphism invariance, and the meaning of coordinates. Pages 105–143 in Lehmkuhl, D, Schiemann, G. & Scholz, E. (Eds.), Towards a Theory of Spacetime Theories. Einstein Studies, vol. 13. Birkhauser.Google Scholar
Redhead, M. (2002). The interpretation of gauge symmetry. In Kuhlmann, M., Lyre, H., & Wayne, A. (Eds.), Ontological Aspects of Quantum Field Theories (pp. 281–302). World Scientific.Google Scholar
Rickles, D. (2017). Dual theories: “Same but different” or “different but same”? Studies in History and Philosophy of Modern Physics, 59, 62–67.Google Scholar
Riello, A. (2020). Soft charges from the geometry of field space. Journal of High Energy Physics, 2020, 125. doi: https://doi.org/10.1007/JHEP05(2020)125.Google Scholar
Roberts, B. (2013). The simple failure of Curie’s principle. Philosophy of Science, 80(4), 579–592.Google Scholar
Rohrlich, F. (2007). Classical Charged Particles (3rd ed.). World Scientific. doi: https://doi.org/10.1142/6220.Google Scholar
Ross, D. (1973). Renormalization of a spontaneous symmetry-breaking model in the unitary gauge. Nuclear Physics B, 59, 23–33.Google Scholar
Rosten, O. J. (2012). Fundamentals of the Exact Renormalization Group. Physics Reports, 511, 177–272. doi: https://doi.org/10.1016/j.physrep.2011.12.003.Google Scholar
Ruegg, H., & Ruiz-Altaba, M. (2004). The Stueckelberg field. International Journal of Modern Physics A, 19, 3265–3347.Google Scholar
Ryckman, T. (2005). The Reign of Relativity: Philosophy in Physics 1915–1925. Oxford University Press.Google Scholar
Ryckman, T. (2020). The gauge principle, Hermann Weyl, and symbolic construction from the “purely infinitesimal.” Pages 179–201 in Wiltsche, H. & Berghofer, P. (Eds.), Phenomenological Approaches to Physics. Synthese Library, vol. 429. Springer.Google Scholar
Sannino, F. (2009). Conformal dynamics for TeV physics and cosmology. Acta Physica Polonica, B40, 3533–3743. (Technicolor)Google Scholar
Sartori, G. (1991). Geometric invariant theory: A model independent approach to spontaneous symmetry and/or supersymmetry breaking. La Rivista del Nuovo Cimento, 14N11, 1–120. doi: https://doi.org/10.1007/BF02810048.Google Scholar
Saunders, S. (2003). Physics and Leibniz’s principles. Pages 289–308 in Brading, K. & Castellani, E. (Eds.), Symmetries in Physics: Philosophical Reflections. Cambridge University Press.Google Scholar
Scholz, E. (2004). Hermann Weyl’s analysis of the “problem of space” and the origin of gauge structures. Science in Context, 17(1–2), 165–197. doi: https://doi.org/10.1017/S0269889704000080.Google Scholar
Scholz, E. (2020). Gauging the spacetime metric: Looking back and forth a century later. Fundamental Theories of Physics, 199, 25–89. doi: https://doi.org/10.1007/978-3-030-51197-5/2.Google Scholar
Sharpe, R. W. (1996). Differential Geometry: Cartan’s Generalization of Klein’s Erlangen Program. (Vol. 166). Springer.Google Scholar
Shaw, R. (1955). The problem of particle types and other contributions to the theory of elementary particles. (Unpublished doctoral dissertation). University of Cambridge.Google Scholar
Singer, I. M. (1978). Some remarks on the Gribov ambiguity. Communications in Mathematical Physics, 60, 7–12.Google Scholar
Smeenk, C. (2006). The elusive Higgs mechanism. Philosophy of Science, 73(5), 487–499.Google Scholar
Sondenheimer, R. (2020). Analytical relations for the bound state spectrum of gauge theories with a Brout–Englert–Higgs mechanism. Physical Review D, 101(5), 056006. doi: https://doi.org/10.1103/PhysRevD.101.056006.Google Scholar
Speranza, A. (2018). Local phase space and edge modes for diffeomorphism-invariant theories. Journal of High Energy Physics, 2018(2), 21.Google Scholar
Steiner, M. (1989). The application of mathematics to natural science. Journal of Philosophy, 86(9), 449–480.Google Scholar
Steiner, M. (1998). The applicability of mathematics as a philosophical problem. Harvard University Press.Google Scholar
Stora, R. (1984). Algebraic structure and topological origin of chiral anomalies. Pages 543–562 in ’t Hooft, G. & et al. (Eds.), Progress in Gauge Field Theory. Plenum Press.Google Scholar
Strocchi, F., & Wightman, A. S. (1973). Proof of the charge superselection rule in local relativistic quantum field theory. Journal of Mathematical Physics, 15(12), 2198–2224. doi: https://doi.org/10.1063/1.1666601.Google Scholar
Struyve, W. (2011). Gauge invariant accounts of the Higgs mechanism. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 42(4), 226–236.Google Scholar
Stueckelberg, E. (1938a). Interaction energy in electrodynamics and in the field theory of nuclear forces. Helvetica Physica Acta, 11, 225–244.Google Scholar
Stueckelberg, E. (1938b). Interaction forces in electrodynamics and in the field theory of nuclear forces. Helvetica Physica Acta, 11, 299–328.Google Scholar
Teh, N. J. (2016). Galileo’s gauge: Understanding the empirical significance of gauge symmetry. Philosophy of Science, 83(1), 93–118. doi: https://doi.org/10.1086/684196.Google Scholar
Teller, P. (1997). A metaphysics for contemporary field theories – essay review: Sunny Y. Auyang, How Is Quantum Field Theory Possible? Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 28(4), 507–522.Google Scholar
Törek, P., Maas, A., & Sondenheimer, R. (2018). A study of how the particle spectra of SU(N) gauge theories with a fundamental Higgs emerge. EPJ Web of Conferences, 175, 08002. doi: https://doi.org/10.1051/epjconf/201817508002.Google Scholar
Trautman, A. (1979). General Fibre bundles, gauge fields, and gravitation. Pages 287–308 in General Relativity and Gravitation. Plenum Press.Google Scholar
Utiyama, R. (1956). Invariant theoretical interpretation of interaction. Physical Review, 101, 1597–1607.Google Scholar
Vaidman, L. (2012). Role of potentials in the Aharonov–Bohm effect. Physical Review A, 86(4), 040101.Google Scholar
Vaidman, L. (2015). Reply to ”Comment on ‘Role of potentials in the Aharonov–Bohm effect’.” Physical Review A, 92(2), 26102.Google Scholar
Vandersickel, N., & Zwanziger, D. (2012). The Gribov problem and QCD dynamics. Physics Reports, 520, 175–251. doi: https://doi.org/10.1016/j.physrep.2012.07.003.Google Scholar
Wallace, D. (2014). Deflating the Aharonov-Bohm effect. https://arxiv.org/abs/1407.5073.Google Scholar
Wallace, D. (2022a). Isolated systems and their symmetries, part I: General framework and particle-mechanics examples. Studies in History and Philosophy of Science, 92, 239–248.Google Scholar
Wallace, D. (2022b). Isolated systems and their symmetries, part II: Local and global symmetries of field theories. Studies in History and Philosophy of Science, 92, 249–259.Google Scholar
Weinberg, S. (2000). The Quantum Theory of Fields. Vol. 3: Supersymmetry. Cambridge University Press.Google Scholar
Westenholz, C. V. (1980a). On spontaneous symmetry breakdown and the Higgs mechanism. Acta Physica Academia Scientiarum Hungaricae, 48, 213–224.Google Scholar
Westenholz, C. V. (1980b). On spontaneous symmetry breakdown and the Higgs mechanism. Acta Physica Academia Scientiarum Hungaricae, 48, 213–224.Google Scholar
Weyl, H. (1918). Gravitation and electricity. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin, 26, 465–480.Google Scholar
Weyl, H. (1929a). Elektron und Gravitation. I. Zeitschrift für Physik A Hadrons and Nuclei, 56(5), 330–352.Google Scholar
Weyl, H. (1929b). Gravitation and the electron. Proceedings of the National Academy of Sciences, 15(4), 323–334.Google Scholar
Wheeler, J. A., & Feynman, R. P. (1949). Classical electrodynamics in terms of direct interparticle action. Reviews of Modern Physics, 21, 425–433. doi: https://doi.org/10.1103/RevModPhys.21.425.Google Scholar
Wigner, E. P. (1967a). Events, laws of nature, and invariance principles. In Symmetries and Reflections: Scientific Essays of Eugene P. Wigner. Indiana University Press.Google Scholar
Wigner, E. P. (1967b). Symmetry and conservation laws. In Symmetries and Reflections: Scientific Essays of Eugene P. Wigner. Indiana University Press.Google Scholar
Wise, D. K. (2009). Symmetric space, Cartan connections and gravity in three and four dimensions. SIGMA, 5, 080–098.Google Scholar
Wise, D. K. (2010). MacDowell–Mansouri gravity and Cartan geometry. Classical and Quantum Gravity, 27, 155010.Google Scholar
Woodhouse, K. A. (1974). Renormalizability of the unitary gauge. Il Nuovo Cimento A (1965–1970), 23(3), 459–493.Google Scholar
Wu, T. T., & Yang, C. N. (1975). Concept of nonintegrable phase factors and global formulation of gauge fields. Physical Review D, 12(12), 3845.Google Scholar
Yang, C.-N. (1980). Einstein’s impact on theoretical physics. Physics Today, 33(6), 42–49.Google Scholar
Yang, C.-N. (1996). Symmetry and physics. Proceedings of the American Philosophical Society, 140(3), 267–288.Google Scholar
Yang, C.-N., & Mills, R. L. (1954). Conservation of isotopic spin and isotopic gauge invariance. Physical Review, 96(1), 191.Google Scholar
Yndurain, F. J. (2006). The Theory of Quark and Gluon Interactions. Springer. doi: https://doi.org/10.1007/3-540-33210-3.Google Scholar
Zee, A. (2010). Quantum Field Theory in a Nutshell (2nd ed.). Princeton University Press.Google Scholar
Zyla, P., et al. (2020). Review of particle physics. PTEP, 2020(8), 083C01. doi: https://doi.org/10.1093/ptep/ptaa104.Google Scholar
- 2
- Cited by