Straightforward Hamiltonian analysis of $BF$ gravity in $n$ dimensions

Abstract

We perform, in a manifestly $SO(n-1,1)$ [$SO(n)$] covariant fashion, the Hamiltonian analysis of general relativity in $n$ dimensions written as a constrained $BF$ theory. We solve the constraint on the $B$ field in a way naturally adapted to the foliation of the spacetime that avoids explicitly the introduction of the vielbein. This leads to a form of the action involving a presymplectic structure, which is reduced by doing a suitable parametrization of the connection and then, after integrating out some auxiliary fields, the Hamiltonian form involving only first-class constraints is obtained.

arXiv commentIt matches published version. arXiv admin note: text overlap with arXiv:2010.14526

References in corpus (6)

• New Variables for Classical and Quantum Gravity in all Dimensions I. Hamiltonian Analysis
• New Variables for Classical and Quantum Gravity in all Dimensions II. Lagrangian Analysis
• $BF$ gravity
• Canonical analysis of $n$-dimensional Palatini action without second-class constraints
• Canonical analysis of Holst action without second-class constraints
• Canonical analysis with no second-class constraints of $BF$ gravity with Immirzi parameter

Cited by in corpus (2)

• Trace-free Einstein gravity as two interacting constrained $BF$ theories
• Towards a de Sitter quintom-like cosmology from a reduction of a 7-dimensional $BF$ theory