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

Motomu Tsuda
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Abstract

We generalize the Lagrangian of N = 1 supergravity (SUGRA) by using an arbitrary parameter $ξ$, which corresponds to the inverse of Barbero's parameter $β$. This generalized Lagrangian involves the chiral one as a special case of the value $ξ= \pm i$. 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 $β(=ξ^{-1})$. We give some comments on the canonical formulation of the theory.

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Motomu Tsuda. 1999-06-16. Generalized Lagrangian of N = 1 supergravity and its canonical constraints with the real Ashtekar variable. https://doi.org/10.1103/physrevd.61.024025

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