Abstract
We generalize the Lagrangian of supergravity (SUGRA) by using an arbitrary parameter which corresponds to the inverse of Barbero’s parameter This generalized Lagrangian involves the chiral one as a special case of the value We show that the generalized Lagrangian gives the canonical formulation of SUGRA with the real Ashtekar variable after the decomposition of spacetime. This canonical formulation is also derived from those of the usual SUGRA by performing Barbero’s type canonical transformation with an arbitrary parameter We give some comments on the canonical formulation of the theory.
- Received 25 May 1999
DOI:https://doi.org/10.1103/PhysRevD.61.024025
©1999 American Physical Society