Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-03-03
Phys.Rev. D62 (2000) 064020
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
19 pages, Latex, corrected some typos and added a reference
Scientific paper
10.1103/PhysRevD.62.064020
We reconstruct the Ashtekar's canonical formulation of N = 2 supergravity (SUGRA) starting from the N = 2 chiral Lagrangian derived by closely following the method employed in the usual SUGRA. In order to get the full graded algebra of the Gauss, U(1) gauge and right-handed supersymmetry (SUSY) constraints, we extend the internal, global O(2) invariance to local one by introducing a cosmological constant to the chiral Lagrangian. The resultant Lagrangian does not contain any auxiliary fields in contrast with the 2-form SUGRA and the SUSY transformation parameters are not constrained at all. We derive the canonical formulation of the N = 2 theory in such a manner as the relation with the usual SUGRA be explicit at least in classical level, and show that the algebra of the Gauss, U(1) gauge and right-handed SUSY constraints form the graded algebra, G^2SU(2)(Osp(2,2)). Furthermore, we introduce the graded variables associated with the G^2SU(2)(Osp(2,2)) algebra and we rewrite the canonical constraints in a simple form in terms of these variables. We quantize the theory in the graded-connection representation and discuss the solutions of quantum constraints.
Shirafuji Takeshi
Tsuda Motomu
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