Abstract
In this article we investigate charged particles in gauge theories. After reviewing the physical and theoretical problems, a method to construct charged particles is presented. Explicit solutions are found in the abelian theory and a physical interpretation is given. These solutions and our interpretation of these variables as the true degrees of freedom for charged particles, are then tested in the perturbative domain and are demonstrated to yield infra-red finite, on-shell Green’s functions at all orders of perturbation theory. The extension to collinear divergences is studied and it is shown that this method applies to the case of massless charged particles. The application of these constructions to the charged sectors of the standard model is reviewed and we conclude with a discussion of the successes achieved so far in this programme and a list of open questions.
Similar content being viewed by others
References
E P Wigner,Ann. Math. 40, 149 (1939)
S Weinberg,The quantum theory of fields (Cambridge University Press, Cambridge, 1995)
D BuchholzPhys. Lett. B174, 331 (1986)
P Kulish and L Faddeev,Theor. Math. Phys. 4, 745 (1970)
M Lavelle and D McMullan,Phys. Rep. 279, 1 (1997), hep-ph/9509344
M Ciafaloni, inQuantum chromodynamics, Edited by A H Mueller (World Scientific, Singapore, 1989)
V D Duca, L Magnea, and G Sterman,Nucl. Phys. B324, 391 (1989)
For this reason one sometimes speaks of mass singularities
UKQCD, D S Henty, O Oliveira, C Parrinello and S Ryan,Phys. Rev. D54, 6923 (1996), hep-lat/9607014
S A Gogilidze, A M Khvedelidze, D M Mladenov and H P Pavel,Hamiltonian reduction of SU(2) Dirac Yang-Mills mechanics, (1997), hep-th/9707136
D Maison and D Zwanziger,Nucl. Phys. B91, 425 (1975)
H Fröhlich, G Morchio and F Strocchi,Phys. Lett. B89, 61 (1979)
D Zwanziger,Phys. Rev. D11, 3504 (1975)
D Zwanziger,Phys. Rev. D11, 3481 (1975)
G Morchio and F Strocchi,Nucl. Phys. B211, 471 (1983)
D Buchholz,Nucl. Phys. B469, 333 (1996), hep-th/9511002
But not globally gauge invariant.
P A M Dirac,Can. J. Phys. 33, 650 (1955)
E d’Emilio and M Mintchev,Fortschr. Phys. 32, 473 (1984)
E d’Emilio and M Mintchev,Fortschr. Phys. 32 503 (1984)
O Steinmann,Ann. Phys. 157, 232 (1984)
L V Prokhorov and S V Shabanov,Int. J. Mod. Phys. A7, 7815 (1992)
L V Prokhorov, D V Fursaev and S V Shabanov,Theor. Math. Phys. 97, 1355 (1993)
T Kawai and H P Stapp,Phys. Rev. D52, 2517 (1995), quant-ph/9502007
T Kawai and H P Stapp,Phys. Rev. D52, 2505 (1995).
T Kawai and H P Stapp,Phys. Rev. D52, 2484 (1995), quant-ph/9503002
L Lusanna and P Valtancoli,Int. J. Mod. Phys. A12, 4769 (1997), hep-th/9606078
L Lusanna and P Valtancoli,Int. J. Mod. Phys. A12, 4797 (1997), hep-th/9606079
T Kashiwa and N Tanimura,Phys. Rev. D56, 2281 (1997), hep-th/9612250
T Kashiwa and N Tanimura,Physical states and gauge independence of the energy momentum tensor in quantum electrodynamics, (1996), hep-th/9605207.
G Chechelashvili, G Jorjadze, and N Kiknadze,Theor. Math. Phys. 109, 1316 (1997), hep-th/9510050
P Haagensen and K Johnson,On the wave functional for two heavy color sources in Yang-Mills theory, (1997), hep-th/9702204
For details, see Sect. 7 of [5] and [30]
K Cahill and D R Stump,Phys. Rev. D20, 540 (1979)
J Dollard,J. Math. Phys. 5, 729 (1964)
A fuller account of this derivation of the asymptotic interaction will be presented in § 5 as part of a more general analysis that includes the case of massless matter
N N Bogolyubov and D V Shirkov
In non-abelian gauge theories the gauge field also needs to be dressed in order for it to carry
M Lavelle and D McMullan,Phys. Lett. B371, 83 (1996), hep-ph/9509343
M Lavelle and D McMullan,Phys. Lett. B329, 68 (1994), hep-th/9403147
The non-abelian appearance of this gauge transformation in QED arises from the fact that the dressing is field dependent and thus might not commute with the potential
E Bagan, M Lavelle, and D McMullan hep-th/9712080, to appear inPhys. Rev. D [RC] (1997)
R Haag,Local quantum physics: fields, particles, algebras (Springer, Berlin, 1992)
H Georgi,Phys. Lett. B240, 447 (1990)
G Sterman,An introduction to quantum field theory (Cambridge University Press, Cambridge, 1993).
E Bagan, M Lavelle, and D McMullan,Phys. Rev. D56, 3732 (1997), hep-th/9602083
E Bagan, B Fiol, M Lavelle, and D McMullan,Mod. Phys. Lett. A12, 1815 (1997), hep-ph/9706515, Erratum-ibid, A12 (1997) 2317
T Muta,Foundations of quantum chromodynamics (World Scientific, Singapore, 1987)
The Feynman rule for the vertex with the source is here taken to be unity for simplicity, it could also be given the renormalisation group invariant form, m2ϕ*ϕ
It is easy to check that the phase part of the dressing does not bring in any soft divergences
Note that the massless tadpole diagrams of figure 5(b) do not cancel, but they, of course, do not alter the on-shell dependence of the IR-structure
R Jackiw and L Soloviev,Phys. Rev. 27, 1485 (1968)
Y L Dokshitser, V A Khoze, A H Mueller, and S I Troian,Basics of perturbative QCD (Ed. Frontieres, Gif-sur-Yvette, France, 1991)
R Doria, J Frenkel, and J C Taylor,Nucl. Phys. B168, 93 (1980)
C Di’Lieto, S Gendron, I G Halliday and C T Sachrajda,Nucl. Phys. B183, 223 (1981)
D Espriu and R Tarrach,Phys. Lett. B383, 482 (1996), hep-ph/9604431
F Havemann,Collinear divergences and asymptotic states, Zeuthen Report No. PHE-85-14, 1985 (unpublished), scanned at KEK
M Nowakowski and A Pilaftsis,Z. Phys. C60, 121 (1993), hep-ph/9305321
G S Jones,Generalised functions, First ed. (McGraw-Hill, Berkshire, 1966)
R Jackiw, D Kabat and M Ortiz,Phys. Lett. B277, 148 (1992)
I Robinson and D Rozga,J. Math. Phys. 25, 499 (1984)
V N Gribov,Nucl. Phys. B139, 1 (1978)
I M Singer,Commun. Math. Phys. 60, 7 (1978)
M Lavelle and D McMullan,Phys. Lett. B347, 89 (1995), hep-th/9412145
L Chen, M Belloni, and K Haller,Phys. Rev. D55, 2347 (1997), hep-ph/9609507
V A Khoze and W Ochs,Int. J. Mod. Phys. A12, 2949 (1997), hep-ph/9701421
C Parrinello, S Petrarca, and A VladikasPhys. Lett. B268, 236 (1991)
P de Forcrand and J E Hetrick,Nucl. Phys. Proc. Suppl. 42, 861 (1995), hep-lat/9412044.
R G Stuart,Unstable particles, (1995), hep-ph/9504308
J Papavassiliou and A Pilaftsis,Phys, Rev. Lett. 75, 3060 (1995), hep-ph/9506417
N Seiberg and E Witten,Nucl. Phys. B426, 19 (1994), hep-th/9407087
M Lavelle and D McMullan,Phys. Rev. Lett. 71, 3758 (1993), hep-th/9306132
I Bialynicki-Birula and Z Bialynicka-Birula,Quantum electrodynamics (Pergamon Press, Oxford, 1975)
Author information
Authors and Affiliations
Corresponding author
Additional information
An erratum to this article is available at http://dx.doi.org/10.1007/BF02831497.
Rights and permissions
About this article
Cite this article
Horan, R., Lavelle, M. & Mcmullan, D. Charges in gauge theories. Pramana - J Phys 51, 317–355 (1998). https://doi.org/10.1007/BF02828927
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02828927