Note About Canonical Formalism for Gravity with Dynamical Determinant of Metric

TL;DR

This paper performs a canonical analysis of a gravity theory with a dynamical metric determinant, exploring its Hamiltonian structure and constraints under restricted diffeomorphism invariance.

Contribution

It introduces a canonical framework for gravity theories where the metric determinant is dynamical, analyzing the resulting Hamiltonian and constraints.

Findings

Derived the Hamiltonian for the theory

Identified the structure of constraints

Explored implications of restricted diffeomorphism invariance

Abstract

In this short note we perform canonical analysis of the theory invariant under restricted diffeomorphism so that the action contains kinetic term for determinant of metric. We find corresponding Hamiltonian and determine structure of constraints.