Hamiltonian dynamics in extended phase space for gravity and its consistency with Lagrangian formalism: a generalized spherically symmetric model as an example

TL;DR

This paper explores a Hamiltonian formulation of gravity using extended phase space, demonstrating its consistency with the Lagrangian approach through a generalized spherically symmetric model and constructing a BRST charge for gauge transformations.

Contribution

It applies the extended phase space Hamiltonian approach to a generalized spherically symmetric gravity model, ensuring consistency with Lagrangian formalism and deriving a BRST charge for gauge invariance.

Findings

Successful formulation of Hamiltonian dynamics in extended phase space for gravity.

Construction of a BRST charge that generates correct gauge transformations.

Validation of the approach using a generalized spherically symmetric model.

Abstract

Among theoretical issues in General Relativity the problem of constructing its Hamiltonian formulation is still of interest. The most of attempts to quantize Gravity are based upon Dirac generalization of Hamiltonian dynamics for system with constraints. At the same time there exists another way to formulate Hamiltonian dynamics for constrained systems guided by the idea of extended phase space. We have already considered some features of this approach in the previous MG12 Meeting by the example of a simple isotropic model. Now we apply the approach to a generalized spherically symmetric model which imitates the structure of General Relativity much better. In particular, making use of a global BRST symmetry and the Noether theorem, we construct the BRST charge that generates correct gauge transformations for all gravitational degrees of freedom.