Generalized Lagrangian of N = 1 supergravity and its canonical constraints with the real Ashtekar variable

Details Generalized Lagrangian of N = 1 supergravity and its canonical constraints with the real Ashtekar variable Generalized Lagrangian of N = 1 supergravity and its canonical constraints with the real Ashtekar variable

1999-06-16

arxiv.org/abs/gr-qc/9906057v1

Phys.Rev. D61 (2000) 024025

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, LATEX

Scientific paper

10.1103/PhysRevD.61.024025

We generalize the Lagrangian of N = 1 supergravity (SUGRA) by using an arbitrary parameter $\xi$, which corresponds to the inverse of Barbero's parameter $\beta$. This generalized Lagrangian involves the chiral one as a special case of the value $\xi = \pm i$. We show that the generalized Lagrangian gives the canonical formulation of N = 1 SUGRA with the real Ashtekar variable after the 3+1 decomposition of spacetime. This canonical formulation is also derived from those of the usual N = 1 SUGRA by performing Barbero's type canonical transformation with an arbitrary parameter $\beta (=\xi^{-1})$. We give some comments on the canonical formulation of the theory.

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