Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Additional SUSY and SUGRA Issues

  • Chapter
  • First Online:
Quantum Cosmology - The Supersymmetric Perspective - Vol. 2

Part of the book series: Lecture Notes in Physics ((LNP,volume 804))

  • 1114 Accesses

Abstract

Two frameworks associated with supersymmetry (SUSY) will be the focus of this chapter, with a view to their further application in probing SQC. These are SUSY breaking (see Sects. 3.1 and 3.2) [1–9] and supersymmetric quantum mechanics (SQM) (see Sect. 3.3) [10–70]. Neither of them has been much investigated in SQC, although the latter feature could be associated with the SQC approach introduced in Chap. 6 of Vol. I.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    \({\boldsymbol{\xi}} ^{(a)}=0\) if \((a)\) does not take values in an Abelian factor of the gauge group.

  2. 2.

    With a minimum of V such that \(\langle f^{\mathsf{I}}\rangle \ne 0\) or \(\langle {\mathsf{d}}^{(a)}\rangle \ne 0\), or in other words, no vacuum with \(\langle f^{{\mathsf{I}}}\rangle =\langle {\mathsf{d}}^{(a)}\rangle =0\), i.e., no solution \(\langle \phi^{{\mathsf{I}}}\rangle \) to these equations.

  3. 3.

    Here, q i are the U(1) charges of \(\phi^{{\mathsf{I}}}\).

  4. 4.

    The SUGRA action depends only on the functions \({\mathsf{G}}(\phi ^{*},\phi )\) and \( {\textrm{f}}_{(a)(b)}(\phi )\), whereas in the global SUSY case we had to define the input of \({\mathsf{K, W,}}\) and f. Hence, coupled to gravity, the kinetic function \({\mathsf{K}},\) and the superpotential \({\mathsf{W}}\) lose their independent meaning and combine to \({\mathsf{G}}(\phi ^{*},\phi)\), which determines the Kähler manifold with \({\mathsf{G}}\) now the Kähler potential (see Sect. 3.5 of Vol. I).

  5. 5.

    Hence, in SUGRA theories, one can find a mechanism to tune the cosmological constant to any chosen value: SUSY breaks if one or more auxiliary fields are non-zero at the vacuum. At the vacuum with unbroken SUSY, we have a cosmological constant given by

    $$\varLambda \sim -\frac{3}{{{\relax\ifmmode\mathsf{k}\else\textsf{k}\fi}} ^{4}}\left\langle {\mathrm{e}}^{{\mathsf{G}}}\right\rangle\;,$$

    hence determining a Minkowski or anti-de Sitter space. Phenomenology requires SUSY to be broken, and also a small cosmological constant. These are non-trivial conditions on \(\mathsf{G}\).

  6. 6.

    Recall that this is another superspace, not that of the full function space [i.e., superspace (see Chap. 2)] of all 3-metrics on a spacelike 3-surface embedded in spacetime.

  7. 7.

    Here we introduce the notation as given in [81, 82, 83, 84, 85], which is different from the usual notation of SUSY field theory in 2-spinor form. This choice is inherited from a 4-spinor notation (see Note A.6 in Appendix A), and is widely followed in most of the literature referring to the context in Chap. 8.

  8. 8.

    The Lagrangian can be obtained by dimensional reduction of the N = 1 sigma model in 1 + 1 dimensions.

  9. 9.

    We define the fermion Fock vacuum by \(| 0 \rangle\) and the completely filled fermion state by \(| \varPsi_n \rangle \), where

    $$\chi^x|0\rangle = 0\;, \qquad\bar\chi^x|\varPsi_n\rangle = 0 \mbox{for all}\;\, x\;,$$
    ((3.80))

    the former being trivially annihilated by \(\mathcal{S}\) and the latter by \(\bar {\mathcal{S}}\). Note also that [see (3.79) above]

    $$\begin{array}{*{20}l} |\varPsi_n\rangle &=& \frac{1}{n!}\epsilon_{x_1\ldots x_n} \bar{\chi}^{x_1}\ldots\bar{\chi}^{x_n}|0\rangle \\ &=& \frac{1}{n!}\sqrt{|\det({\mathcal{G}}_{XY})|} \epsilon_{X_1\ldots X_n}\bar{\chi}^{X_1} \ldots\bar{\chi}^{X_n}|0\rangle\;.\end{array}$$
    ((3.81))
  10. 10.

    Boundaries (e.g., 3-manifolds) are important when dealing with quantum amplitudes, and so cannot be neglected in off-shell situations (see Note 2.3 in Vol. I).

References

  1. Bailin, D., Love, A.: Supersymmetric Gauge Field Theory and String Theory. Graduate Student Series in Physics, 322pp. IOP, Bristol (1994)

    Book  Google Scholar 

  2. Bilal, A.: Introduction to supersymmetry. hep-th/0101055 (2001)

    Google Scholar 

  3. Figueroa-O’Farrill, J.M.: BUSSTEPP lectures on supersymmetry. hep-th/0109172 (2001)

    Google Scholar 

  4. Martin, S.P.: A supersymmetry primer. hep-ph/9709356 (1997)

    Google Scholar 

  5. Muller-Kirsten, H.J.W., Wiedemann, A.: Supersymmetry: An introduction with conceptual and calculational details, pp. 1–586. World Scientific (1987). Print-86–0955 (Kaiserslautern) (1986)

    Google Scholar 

  6. Nilles, H.P.: Supersymmetry, supergravity and particle physics. Phys. Rep. 110, 1 (1984)

    Article  ADS  Google Scholar 

  7. Sohnius, M.F.: Introducing supersymmetry. Phys. Rep. 128, 39–204 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  8. Srivastava, P.P.: Supersymmetry, Superfields, and Supergravity: An Introduction. Graduate Student Series in Physics, 162pp. Hilger, Bristol (1986)

    Google Scholar 

  9. Terning, J.: Modern Supersymmetry: Dynamics and Duality, p. 324. Clarendon Press, Oxford (2006)

    MATH  Google Scholar 

  10. Brink, L., Henneaux, M., Teitelboim, C.: Covariant Hamiltonian formulation of the superparticle. Nucl. Phys. B 293, 505–540 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  11. Campostrini, M., Wosiek, J.: High precision study of the structure of D = 4 supersymmetric Yang–Mills quantum mechanics. Nucl. Phys. B 703, 454–498 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Campostrini, M., Wosiek, J.: Exact Witten index in D = 2 supersymmetric Yang–Mills quantum mechanics. Phys. Lett. B 550, 121–127 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Capdequi-Peyranere, M.: Is supersymmetric quantum mechanics compatible with duality? Mod. Phys. Lett. A 14, 2657–2666 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  14. Cappiello, L., D’Ambrosio, G.: Supersymmetric dissipative quantum mechanics from superstrings. J. High Energy Phys. 07, 002 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  15. Carlitz, R.D.: Classical paths in supersymmetric quantum mechanics. Z. Phys. C 26, 581 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  16. Chandia, O., Zanelli, J.: Supersymmetric particle in a spacetime with torsion and the index theorem. Phys. Rev. D 58, 045014 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  17. Combescure, M., Gieres, F., Kibler, M.: Are N = 1 and N = 2 supersymmetric quantum mechanics equivalent? quant-ph/0401120 (2004)

    Google Scholar 

  18. Comtet, A., Bandrauk, A.D., Campbell, D.K.: Exactness of semiclassical bound state energies for supersymmetric quantum mechanics. Phys. Lett. B 150, 159–162 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  19. Cooper, F., Freedman, B.: Aspects of supersymmetric quantum mechanics. Ann. Phys. 146, 262 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  20. Daoud, M., Kibler, M.: Fractional supersymmetric quantum mechanics as a set of replicas of ordinary supersymmetric quantum mechanics. Phys. Lett. A 321, 147–151 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. Davis, A.C., Macfarlane, A.J., Popat, P., van Holten, J.W.: The quantum mechanics of the supersymmetric onlinear sigma model. J. Phys. A 17, 2945 (1984) 35

    Article  MathSciNet  ADS  Google Scholar 

  22. de Crombrugghe, M., Rittenberg, V.: Supersymmetric quantum mechanics. Ann. Phys. 151, 99 (1983)

    Article  ADS  Google Scholar 

  23. de Lima Rodrigues, R., Bezerra, V.B., Vaidya, A.N.: An application of supersymmetric quantum mechanics to a planar physical system. Phys. Lett. A 287, 45–49 (2001)

    Article  ADS  MATH  Google Scholar 

  24. Deotto, E., Gozzi, E.: On the ‘universal’ N = 2 supersymmetry of classical mechanics. Int. J. Mod. Phys. A 16, 2709 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. Deotto, E., Gozzi, E., Mauro, D.: Supersymmetry in classical mechanics. hep-th/0101124 (2001)

    Google Scholar 

  26. Donets, E.E., Pashnev, A., Rivelles, V.O., Sorokin, D.P., Tsulaia, M.: N = 4 superconformal mechanics and the potential structure of AdS spaces. Phys. Lett. B 484, 337–346 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. Faux, M., Spector, D.: Duality and central charges in supersymmetric quantum mechanics. Phys. Rev. D 70, 085014 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  28. Faux, M., Kagan, D., Spector, D.: Central charges and extra dimensions in supersymmetric quantum mechanics. hep-th/0406152 (2004)

    Google Scholar 

  29. Freedman, B., Cooper, F.: Fun with supersymmetric quantum mechanics. Physica D 15, 138 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  30. Gamboa, J., Ramirez, C.: Hamiltonian approach to 2D supergravity. Phys. Lett. B 301, 20–24 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  31. Gamboa, J., Zanelli, J.: Supersymmetric nonrelativistic quantum mechanics. Phys. Lett. B 165, 91–93 (1985)

    Google Scholar 

  32. Gamboa, J., Zanelli, J.: Supersymmetric quantum mechanics of fermions minimally coupled to gauge fields. J. Phys. A 21, L283–L286 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  33. Gamboa, J., Zanelli, J., Ruiz-Altaba, M.: Supersymmetrization of scalar field theories. Phys. Lett. B 206, 252 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  34. Gamboa, J., Zanelli, J.: Ground state and supersymmetry of generally covariant systems. Ann. Phys. 188, 239 (1988)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. Gozzi, E.: Ground state wave function ‘representation’. Phys. Lett. B 129, 432 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  36. Gozzi, E.: The Onsager principle of microscopic reversibility and supersymmetry. Phys. Rev. D 30, 1218 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  37. Gozzi, E.: On the nodal structure of supersymmetric wave functions. Phys. Rev. D 33, 3665 (1986)

    Article  MathSciNet  ADS  Google Scholar 

  38. Gozzi, E.: Comment on ‘on the hidden supersymmetry in stochastic quantization’. Phys. Rev. D 44, 3994–3996 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  39. Gozzi, E.: Universal hidden supersymmetry in classical mechanics and its local extension. hep-th/9703203 (1997)

    Google Scholar 

  40. Grosse, H.: Supersymmetric quantum mechanics. Lectures given at Brasov International School on Recent Developments in Quantum Mechanics, Poiana Brasov, Romania, 29 August–9 September 1989

    Google Scholar 

  41. Henneaux, M., Teitelboim, C.: Relativistic quantum echanics of supersymmetric particles. Ann. Phys. 143, 127 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  42. Hernandez, R., Sfetsos, K.: Supersymmetric quantum mechanics from wrapped branes. Phys. Lett. B 582, 102–112 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  43. Heumann, R., Manton, N.S.: Classical supersymmetric mechanics. Ann. Phys. 284, 52–88 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  44. Macias, A., Obregon, O., Socorro, J.: Supersymmetric quantum cosmology. Int. J. Mod. Phys. A 8, 4291–4317 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  45. Ivanov, E., Lechtenfeld, O.: N = 4 supersymmetric mechanics in harmonic superspace. JHEP 09, 073 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  46. Ivanov, E.A., Krivonos, S.O., Pashnev, A.I.: Partial supersymmetry breaking in N = 4 supersymmetric quantum mechanics. Class. Quant. Grav. 8, 19–40 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  47. Jackiw, R., Polychronakos, A.P.: Supersymmetric fluid mechanics. Phys. Rev. D 62, 085019 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  48. Jaffe, A., Lesniewski, A., Lewenstein, M.: Ground state structure in supersymmetric quantum mechanics. Ann. Phys. 178, 313 (1987)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  49. Kihlberg, A., Salomonson, P., Skagerstam, B.S.: Witten’s index and supersymmetric quantum mechanics. Z. Phys. C 28, 203–209 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  50. Kostelecky, V.A., Nieto, M.M.: Evidence for a phenomenological supersymmetry in atomic physics. Phys. Rev. Lett. 53, 2285 (1984)

    Article  ADS  Google Scholar 

  51. Kostelecky, V.A., Nieto, M.M., Truax, D.R.: Supersymmetry and the relationship between the Coulomb and oscillator problems in arbitrary dimensions. Phys. Rev. D 32, 2627 (1985)

    Google Scholar 

  52. Kotanski, J., Wosiek, J.: Hamiltonian study of supersymmetric Yang–Mills quantum mechanics. Nucl. Phys. Proc. Suppl. 119, 932–934 (2003)

    Article  ADS  MATH  Google Scholar 

  53. Lancaster, D.: Supersymmetry breakdown in supersymmetric quantum mechanics. Nuovo Cim. A 79, 28 (1984)

    Article  ADS  Google Scholar 

  54. Quesne, C., Tkachuk, V.M.: More on a SUSY QM approach to the harmonic oscillator with nonzero minimal uncertainties in position and/or momentum. math-ph/0312029 (2003)

    Google Scholar 

  55. Rietdijk, R.H.: Supersymmetric quantum mechanics and the index theorem. J. Geom. Phys. 11, 545–551 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  56. Salomonson, P., van Holten, J.W.: Fermionic coordinates and supersymmetry in quantum mechanics. Nucl. Phys. B 196, 509 (1982)

    Article  ADS  Google Scholar 

  57. Shabanov, S.V.: On minisuperspace gauge models with fermions. In: Proceedings on Classical and Quantum Gravity, Evora, 1992, pp. 322–331. World Scientific, River Edge, NJ (1993)

    Google Scholar 

  58. Soroka, D.V., Soroka, V.A., Wess, J.: Supersymmetric D = 1, N = 1 model with Grassmann-odd Lagrangian. Phys. Lett. B 512, 197–202 (2001)

    Article  ADS  MATH  Google Scholar 

  59. Soroka, V.A.: On square root of Hamilton’s equations for supersymmetric systems. J. Experiment. Theor. Phys. Lett. 60, 387–392 (1994)

    MathSciNet  ADS  Google Scholar 

  60. Soroka, V.A.: Supersymmetry and the odd Poisson bracket. Nucl. Phys. Proc. Suppl. 101, 26–42 (2001)

    Article  MathSciNet  Google Scholar 

  61. Szwed, J.: The ‘square root’ of the Dirac equation within supersymmetry. Phys. Lett. B 181, 305 (1986)

    Article  MathSciNet  ADS  Google Scholar 

  62. Szwed, J.: The ‘square root’ of the Dirac equation and solutions on superspace. hep-th/0403036 (2004)

    Google Scholar 

  63. Tanimoto, M.: The role of Killing–Yano tensors in supersymmetric mechanics on a curved manifold. Nucl. Phys. B 442, 549–562 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  64. Urrutia, L.F., Zanelli, J.: Local supersymmetry in nonrelativistic systems. J. Math. Phys. 31, 2271–2277 (1990)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  65. Volkov, D.V., Pashnev, A.I., Soroka, V.A., Tkach, V.I.: Hamiltonian systems with even and odd Poisson brackets. Duality of their conservation laws. JETP Lett. 44, 70–72 (1986)

    ADS  Google Scholar 

  66. Witten, E.: Dynamical breaking of supersymmetry. Nucl. Phys. B 188, 513 (1981)

    Article  ADS  MATH  Google Scholar 

  67. Witten, E.: Constraints on supersymmetry breaking. Nucl. Phys. B 202, 253 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  68. Wosiek, J.: Spectra of supersymmetric Yang–Mills quantum mechanics. Nucl. Phys. B 644, 85–112 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  69. Wosiek, J.: Recent progress in supersymmetric Yang–Mills quantum mechanics in various dimensions. Acta Phys. Polon. B 34, 5103–5118 (2003)

    ADS  Google Scholar 

  70. Znojil, M.: Relativistic supersymmetric quantum mechanics based on Klein–Gordon equation. J. Phys. A 37, 9557–9572 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  71. Wess, J., Bagger, J.: Supersymmetry and Supergravity, 259pp. Princeton University Press, Princeton, NJ (1992)

    Google Scholar 

  72. West, P.C.: Introduction to Supersymmetry and Supergravity, 425pp. World Scientific, Singapore (1990)

    MATH  Google Scholar 

  73. Van Nieuwenhuizen, P.: Supergravity. Phys. Rep. 68, 189–398 (1981)

    Article  MathSciNet  ADS  Google Scholar 

  74. Khare, A., Maharana, J.: Supersymmetric quantum mechanics in one dimension, two dimensions, and three dimensions. Nucl. Phys. B 244, 409 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  75. Junker, G.: Supersymmetric Methods in Quantum and Statistical Physics. Texts and Monographs in Physics, 172pp. Springer, Heidelberg (1996)

    Book  Google Scholar 

  76. Cooper, F., Khare, A., Sukhatme, U.: Supersymmetry in Quantum Mechanics, 210pp. World Scientific, Singapore (2001)

    Book  MATH  Google Scholar 

  77. Cooper, F., Khare, A., Sukhatme, U.: Supersymmetry and quantum mechanics. Phys. Rep. 251, 267–385 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  78. Donets, E.E., Pashnev, A., Rosales, J.J., Tsulaia, M.: Partial supersymmetry breaking in multidimensional N = 4 SUSY QM. hep-th/0001194 (1999)

    Google Scholar 

  79. Donets, E.E., Pashnev, A., Juan Rosales, J., Tsulaia, M.M.: N = 4 supersymmetric multidimensional quantum mechanics, partial SUSY breaking and superconformal quantum mechanics. Phys. Rev. D 61, 043512 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  80. Donets, E.E., Pashnev, A.I., Tsulaia, M.M., Sorokin, D.P., Rivelles, V.O.: Potential structure of AdS spaces. Czech. J. Phys. 50, 1215–1220 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  81. Obregon, O., Rosales, J.J., Tkach, V.I.: Superfield description of the FRW universe. Phys. Rev. D 53, 1750–1753 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  82. Tkach, V.I., Obregon, O., Rosales, J.J.: FRW model and spontaneous breaking of supersymmetry. Class. Quant. Grav. 14, 339–350 (1997)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  83. Tkach, V.I., Rosales, J.J.: Supersymmetric action for FRW model with complex matter field. gr-qc/9705062 (1997)

    Google Scholar 

  84. Tkach, V.I., Rosales, J.J., Martinez, J.: Action for the FRW model and complex matter field with local supersymmetry. Class. Quant. Grav. 15, 3755–3762 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  85. Tkach, V.I., Rosales, J.J., Obregon, O.: Supersymmetric action for Bianchi type models. Class. Quant. Grav. 13, 2349–2356 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  86. Duplij, S., Siegel, W., Bagger, J. (eds.): Concise Encyclopedia of Supersymmetry and Noncommutative Structures in Mathematics and Physics. Kluwer Academic Publishers, Dordrecht (2003)

    Google Scholar 

  87. Lidsey, J.E., Wands, D., Copeland, E.J.: Superstring cosmology. Phys. Rep. 337, 343–492 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  88. Claudson, M., Halpern, M.B.: Supersymmetric ground state wave functions. Nucl. Phys. B 250, 689 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  89. Donets, E.E., Tentyukov, M.N., Tsulaia, M.M.: Towards N = 2 SUSY homogeneous quantum cosmology: Einstein–Yang–Mills systems. Phys. Rev. D 59, 023515 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  90. DeWitt, B.S.: Supermanifolds. Cambridge Monographs on Mathematical Physics, 2nd edn., pp. 1–407. Cambridge University Press, Cambridge (1992)

    Google Scholar 

  91. Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation, 1279pp. Freeman, San Francisco (1973)

    Google Scholar 

  92. Farajollahi, H., Luckock, H.: Stochastic quantisation of locally supersymmetric models. gr-qc/0406022 (2004)

    Google Scholar 

  93. Graham, R., Luckock, H.: Nicolai maps for quantum cosmology. Phys. Rev. D 49, 2786–2791 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  94. Luckock, H.: Boundary conditions for Nicolai maps. J. Phys. A 24, L1057–L1064 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  95. Luckock, H.: Boundary terms for globally supersymmetric actions. Int. J. Theor. Phys. 36, 501–508 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  96. Luckock, H., Oliwa, C.: The cosmological probability density function for Bianchi class A models in quantum supergravity. Phys. Rev. D 51, 5483–5490 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  97. Graham, R., Roekaerts, D.: Stochastic representation of arbitrary fermion sectors in supersymmetric quantum mechanics in flat space. Phys. Lett. A 120, 223 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  98. Luckock, D., Oliwa, C.: Quantisation of Bianchi class A models in supergravity and the probability density function of the universe. In: 7th Marcel Grossmann Meeting on General Relativity (MG 7), Stanford, CA, 24–30 July 1994

    Google Scholar 

  99. Graham, C., Roekaerts, D.: A Nicolai map for supersymmetric quantum mechanics on Riemannian manifolds. In: Proceedings on Stochastic Processes–-Mathematics and Physics, Bielefeld, pp. 98–105 and BIBOS 082 (86, REC.AUG.), 8pp. Bielefeld University, Bielefeld (1985)

    Google Scholar 

  100. Graham, R., Roekaerts, D.: Supersymmetric quantum mechanics and stochastic processes in curved configuration space. Phys. Lett. A 109, 436–440 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  101. Graham, R., Roekaerts, D.: Stochastic representation of arbitrary fermion sectors in supersymmetric quantum mechanics on Riemannian manifolds. Phys. Rev. D 34, 2312 (1986)

    Article  MathSciNet  ADS  Google Scholar 

  102. Graham, R., Roekaerts, D.: Stochastic representation of arbitrary fermion sectors in supersymmetric quantum mechanics in flat space. Phys. Lett. A 120, 223 (1987)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Depto. Fisica Rua Marquês d’Avila e Bolama, Universidade da Beira Interior, 6200-307, Covilhã, Portugal

    Paulo Vargas Moniz

Authors
  1. Paulo Vargas Moniz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paulo Vargas Moniz .

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Moniz, P.V. (2010). Additional SUSY and SUGRA Issues . In: Quantum Cosmology - The Supersymmetric Perspective - Vol. 2. Lecture Notes in Physics, vol 804. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11570-7_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-11570-7_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11569-1

  • Online ISBN: 978-3-642-11570-7

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation