Canonical analysis of linearized $\lambda R$ gravity plus a Chern-Simons term

TL;DR

This paper performs a Hamiltonian analysis of linearized $\\lambda R$ gravity with a Chern-Simons term, identifying constraints and degrees of freedom, and comparing theories for different $\\lambda$ values.

Contribution

It provides a detailed Hamiltonian constraint analysis of linearized $\\lambda R$ gravity with a Chern-Simons term, highlighting differences across $\\lambda$ values.

Findings

Identifies first- and second-class constraints for arbitrary $\\lambda$

Reports one physical degree of freedom in the theory

Constructs generalized Dirac brackets after removing second-class constraints

Abstract

The Hamiltonian analysis for the linearized $\lambda R$ gravity plus a Chern-Simons term is performed. The first-class and second-class constraints for arbitrary values of $\lambda$ are presented, and one physical degree of freedom is reported. The second-class constraints are removed, and the corresponding generalized Dirac brackets are constructed; then, the difference between theories with different values of $\lambda$ is remarked.