Unimodular Gravity in Covariant Formalism

TL;DR

This paper explores unimodular gravity within the covariant Weyl-De Donder formalism, deriving Hamiltonians and analyzing the impact of unimodular constraints on the covariant momenta and equations of motion.

Contribution

It introduces a covariant Hamiltonian formulation for unimodular gravity, including the Henneaux-Teitelboim action, and examines the effects of unimodular constraints.

Findings

Derived Hamiltonian for unimodular gravity in covariant formalism

Analyzed the impact of unimodular constraints on covariant momenta

Formulated equations of motion for unimodular gravity

Abstract

In this short note we study unimodular gravity in Weyl-De Donder formalism. We find corresponding Hamiltonian and study consequence of the unimodular constraint on the conjugate covariant momenta. We also find covariant Hamiltonian for Henneaux-Teitelboim unimodular action and study corresponding equations of motion.