Canonical Analysis of Unimodular Gravity

TL;DR

This paper performs a Hamiltonian analysis of Unimodular Gravity by treating it as a constrained version of General Relativity, clarifying its constraint structure and canonical formulation.

Contribution

It provides the first detailed canonical analysis of Unimodular Gravity with the unimodular constraint explicitly incorporated.

Findings

Constraint structure of Unimodular Gravity clarified

Canonical formulation of the theory established

Differences from standard General Relativity identified

Abstract

This short note is devoted to the Hamiltonian analysis of the Unimodular Gravity.We treat the unimodular gravity as General Relativity action with the unimodular constraint imposed with the help of Lagrange multiplier. We perform the canonical analysis of the resulting theory and determine its constraint structure.