Covariant Quantum Gravity I: Covariant Hamiltonian Framework

TL;DR

This paper develops a covariant Hamiltonian formulation of Einstein-Cartan gravity using multisymplectic geometry and d-jet bundles, revealing the gauge structure and constraints algebra of the theory.

Contribution

It introduces a covariant Hamiltonian framework for Einstein-Cartan theory based on multisymplectic geometry and d-jet bundles, clarifying the gauge group and constraints algebra.

Findings

The gauge group is the semidirect product of local Lorentz and diffeomorphism groups.

Vanishing of gauge generators corresponds to Einstein-Cartan equations of motion.

The local constraints form a closed Lie algebra.

Abstract

The first part of the series formulates the Einstein-Cartan theory in the covariant hamiltonian framework. The first section revises the general multisymplectic approach and introduces the notion of the d-jet bundles. Since the whole Standard Model Lagrangian (including gravity) can be written as the functional of the forms, the structure of the d-jet bundles is more appropriate for the covariant hamiltonian analysis than the standard jet bundle approach. The definition of the local covariant Poisson bracket on the space of covariant observables is recalled. The main goal of the work is to show that the gauge group of the Einstein-Cartan theory is given by the semidirect product of the local Lorentz group and the group of spacetime diffeomorphisms. Vanishing of the integral generators of the gauge group is equivalent to equations of motion of the Einstein-Cartan theory and the local constraints algebra is closed Lie algebra.