# Reductions of Topologically Massive Gravity II: First Order Realizations of Second Order Lagrangians

## TL;DR

This paper reformulates second order degenerate Lagrangians in topologically massive gravity into first order forms and analyzes their Hamiltonian structure using Dirac-Bergmann constraints.

## Contribution

It introduces new first order Lagrangian formulations for topologically massive gravity and performs a detailed Hamiltonian analysis of these equivalent models.

## Key findings

- Successful reformulation into first order Lagrangians
- Hamiltonian analysis reveals the constraint structure
- Provides a foundation for quantization approaches

## Abstract

Second order degenerate Cl\`ement and Sar{\i}o\u{g}lu-Tekin Lagrangians are casted into forms of various first order Lagrangians. Hamiltonian analysis of these equivalent formalisms are performed by means of Dirac-Bergmann constraint algorithm.