Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1998-07-21
Phys.Rev. D59 (1999) 023515
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
17 pages, REVTeX, no figures; minor corrections, few ref's added; to appear in Phys. Rev. D58, Dec. 15, 1998 issue
Scientific paper
10.1103/PhysRevD.59.023515
The application of N=2 supersymmetric quantum mechanics for the quantization of homogeneous systems coupled with gravity is discussed. Starting with the superfield formulation of an N=2 SUSY sigma model, Hermitian self-adjoint expressions for quantum Hamiltonians and Lagrangians for any signature of a sigma-model metric are obtained. This approach is then applied to coupled SU(2) Einstein-Yang-Mills (EYM) systems in axially symmetric $Bianchi$-type I, II, VIII, IX, $Kantowski-Sachs$, and closed $Friedmann-Robertson-Walker$ cosmological models. It is shown that all these models admit the embedding into the N=2 SUSY sigma model with the explicit expressions for superpotentials being direct sums of gravitational and Yang-Mills (YM) parts. In addition, the YM parts of superpotentials exactly coincide with the corresponding Chern-Simons terms. The spontaneous SUSY breaking caused by YM instantons in EYM systems is discussed in a number of examples.
Donets Evgeni E.
Tentyukov M. N.
Tsulaia Mirian
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