A Pure Dirac's Method for Husain–kuchar Theory

Abstract

A pure Dirac's canonical analysis, defined in the full phase space for the Husain-Kuchar (HK) model is discussed in detail. This approach allows us to determine the extended action, the extended Hamiltonian, the complete constraint algebra and the gauge transformations for all variables that occur in the action principle. The complete set of constraints defined on the full phase space allow us to calculate the Dirac algebra structure of the theory and a local weighted measure for the path integral quantization method. Finally, we discuss briefly the necessary mathematical structure to perform the canonical quantization program within the framework of the loop quantum gravity approach.

Discrete canonical analysis of three-dimensional gravity with cosmological constant

“…[26][27][28][29] This procedure, will allow us to make a cleaner contact with the discrete version, as in order to obtain a consistent discretization, some of the Lagrange multipliers get determined by the scheme, and the evolution is implemented by a canonical transformation, this means that the set of discrete equations that were formerly incompatible can be solved simultaneously.…”