2+1 Gravity without dynamics

TL;DR

This paper presents a three-dimensional covariant theory with a 2+1 decomposition where the Hamiltonian constraint is absent, exploring its classical and quantum properties compared to standard 2+1 gravity.

Contribution

It introduces a novel 3D covariant theory lacking a Hamiltonian constraint, providing new insights into the structure of 2+1 gravity and its observables.

Findings

Physical observables are explicitly described.

Classical and quantum theories are compared.

The theory differs from standard 2+1 gravity by absence of Hamiltonian constraint.

Abstract

A three dimensional generally covariant theory is described that has a 2+1 canonical decomposition in which the Hamiltonian constraint, which generates the dynamics, is absent. Physical observables for the theory are described and the classical and quantum theories are compared with ordinary 2+1 gravity.