Abstract
A promising line of investigation, following the framework of Chap. 4 in Vol. I, is to try to retrieve (quantum) physical states in canonical quantum N = 1 SUGRA. We will discuss this in Sect. 4.1, where the Carroll–Freedman–Ortiz–Page (CFOP) argument and demonstration are presented [1–3].
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Notes
- 1.
- 2.
In general relativity, [23], we can cancel several boundary terms which occur when varying the metric in the Einstein–Hilbert action [see equation (2.17) in Vol. I] by adding a boundary term which contains the extrinsic curvature of the boundary, viz., \(\int_{\partial {\mathcal{M}}}\sqrt{h}K\). The proposal was to impose the boundary condition that the variations of the metric in the surface vanish, i.e., \(\updelta h_{ij}|_{\partial {\mathcal{M}}} = 0\). But this violates local SUSY if one only admits local boundary conditions (in particular no boundary conditions on curvature components, but only on the fields themselves).
- 3.
We henceforth drop the suffix 2 introduced in Sect. 4.3 of Vol. I.
- 4.
The usual functional Schrödinger equation is found from (4.35) after integration over space.
- 5.
The reader should note the use of \(\mathcal F\) in (4.33) and \({\check{\mathcal F}}\) in (4.29) and (4.37), which may appear together in a few expressions.
References
D’Eath, P.D.: Quantum supergravity via canonical quantization. In: Penrose, R., Isham, C. J. (eds.) Proceedings on Quantum Concepts in Space and Time, Oxford, pp. 341–350 (1984)
D’Eath, P.D.: Supersymmetric Quantum Cosmology, 252pp. Cambridge University Press, Cambridge (1996)
D’Eath, P.D.: The canonical quantization of supergravity. Phys. Rev. D 29, 2199 (1984)
Kiefer, C., Luck, T., Moniz, P.: The semiclassical approximation to supersymmetric quantum gravity. Phys. Rev. D 72, 045006 (2005)
D’Eath, P.D.: Physical states in N = 1 supergravity. Phys. Lett. B 321, 368–371 (1994)
Carroll, S.M., Freedman, D.Z., Ortiz, M.E., Page, D.N.: Bosonic physical states in N = 1 supergravity? gr-qc/941005 (1994)
Carroll, S.M., Freedman, D.Z., Ortiz, M.E., Page, D.N.: Physical states in canonically quantized supergravity. Nucl. Phys. B 423, 661–687 (1994)
Csordas, A., Graham, R.: Exact quantum state for N = 1 supergravity. Phys. Rev. D 52, 6656–6659 (1995)
Moniz, P.V.: Supersymmetric quantum cosmology – shaken not stirred. Int. J. Mod. Phys. A 11, 4321–4382 (1996)
Page, D.N.: Inconsistency of canonically quantized N = 1 supergravity? hep-th/9306032 (1993)
DeWitt, B., Matschull, H.J., Nicolai, H.: Physical states in D = 3, N = 2 supergravity. Phys. Lett. B 318, 115–121 (1993)
Matschull, H.-J.: About loop states in supergravity. Class. Quant. Grav. 11, 2395–2410 (1994)
D’Eath, P.D.: What local supersymmetry can do for quantum cosmology. In: Workshop on Conference on the Future of Theoretical Physics and Cosmology in Honor of Steven Hawking’s 60th Birthday, Cambridge, England, 7–10 January 2002
D’Eath, P.D.: Canonical formulation and finiteness of N = 1 supergravity with supermatter. In: 7th Marcel Grossmann Meeting on General Relativity (MG 7), Stanford, CA, 24–30 July 1994
D’Eath, P.D.: Finite N = 1 supergravity. In: 7th Marcel Grossmann Meeting on General Relativity (MG 7), Stanford, CA, 24–30 July 1994
D’Eath, P.D.: Loop amplitudes in supergravity by canonical quantization. hep-th/9807028 (1998)
Esposito, G., Kamenshchik, A.Yu.: Axial gauge in quantum supergravity. hep-th/9604194 (1996)
Esposito, G., Kamenshchik, A.Yu.: One-loop divergences in simple supergravity: Boundary effects. Phys. Rev. D 54, 3869–3881 (1996)
Esposito, G., Pollifrone, G.: Noncovariant gauges in simple supergravity. Int. J. Mod. Phys. D 6, 479–490 (1997)
Esposito, G.: Local boundary conditions in quantum supergravity. Phys. Lett. B 389, 510–514 (1996)
Van Nieuwenhuizen, P., Vassilevich, D.V.: Consistent boundary conditions for supergravity. Class. Quant. Grav. 22, 5029–5051 (2005)
Hawking, S.W., Page, D.N.: The spectrum of wormholes. Phys. Rev. D 42, 2655–2663 (1990)
Kiefer, C.: Quantum Gravity. International Series of Monographs on Physics vol. 136, 2nd edn, pp. 1–308. Clarendon Press, Oxford (2007)
Wulf, M.: Non-closure of constraint algebra in N = 1 supergravity. Int. J. Mod. Phys. D 6, 107–118 (1997)
D’Eath, P.D.: Supergravity and canonical quantization. Int. J. Mod. Phys. D 5, 609–628 (1996)
Gerlach, U.H.: Derivation of the ten Einstein field equations from the semiclassical approximation to quantum geometrodynamics. Phys. Rev. 177, 1929–1941 (1969)
DeWitt, B.S.: Supermanifolds. Cambridge Monographs on Mathematical Physics, 2nd edn., pp. 1–407. Cambridge University Press, Cambridge (1992)
Alonso-Alberca, N., Lozano-Tellechea, E., Ortin, T.: Geometric construction of Killing spinors and supersymmetry algebras in homogeneous spacetimes. Class. Quant. Grav. 19, 6009–6024 (2002)
Ortin, T.: The supersymmetric vistas of the supergravity landscape. Annalen Phys. 15, 251–263 (2006)
Ortin, T.: Gravity and Strings. Cambridge University Press, Cambridge (2004)
Aichelburg, P.C., Dereli, T.: Exact plane wave solutions of supergravity field equations. Phys. Rev. D 18, 1754 (1978)
Aichelburg, P.C., Dereli, T.: First nontrivial exact solution of supergravity. Czech. J. Phys. B 29, 252–255 (1979)
Aichelburg, P.C., Embacher, F.: Supercharge and background perturbations of multi-black hole systems. Class. Quant. Grav. 2, 65 (1985)
Aichelburg, P.C., Embacher, F.: The exact superpartners of N = 2 supergravity solitons. Phys. Rev. D 34, 3006 (1986)
Aichelburg, P.C., Embacher, F.: Supergravity solitons. IV. Effective soliton interaction. Phys. Rev. D 37, 2132 (1988)
Aichelburg, P.C., Gueven, R.: Supersymmetric black holes in \(N = 2\) supergravity theory. Phys. Rev. Lett. 51, 1613 (1983)
Dereli, T., Aichelburg, P.C.: Exact plane wave solutions of O(2) extended supergravity. Phys. Lett. B 80, 357 (1979)
Pauli, W., Fierz, M.: On relativistic field equations of particles with arbitrary spin in an electromagnetic field. Helv. Phys. Acta 12, 297–300 (1939)
Moniz, P.V.: Can the imprint of an early supersymmetric quantum cosmological epoch be present in our cosmological observations? In: COSMO 97: 1st International Workshop on Particle Physics and the Early Universe, Ambleside, England, 15–19 September 1997
Moniz, P.V.: Origin of structure in a supersymmetric quantum universe. Phys. Rev. D 57, 7071–7074 (1998)
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Moniz, P.V. (2010). Semiclassical N=1 Supergravity. 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_4
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