# Hamiltonian Analysis In New General Relativity

## TL;DR

This paper explores the Hamiltonian formulation of new general relativity, a class of theories based on torsion, revealing nine distinct constraint combinations and their impact on the theory's canonical structure.

## Contribution

It provides the explicit ADM Lagrangian for new general relativity and analyzes how different constraint combinations affect the Hamiltonian formulation.

## Key findings

- Nine different constraint combinations lead to distinct theories.
- The inversion of velocities depends on the specific constraint combination.
- The Hamiltonian structure varies with the choice of torsion coefficients.

## Abstract

It is known that one can formulate an action in teleparallel gravity which is equivalent to general relativity, up to a boundary term. In this geometry we have vanishing curvature, and non-vanishing torsion. The action is constructed by three different contractions of torsion with specific coefficients. By allowing these coefficients to be arbitrary we get the theory which is called `new general relativity'. In this note, the Lagrangian for new general relativity is written down in ADM-variables. In order to write down the Hamiltonian we need to invert the velocities to canonical variables. However, the inversion depends on the specific combination of constraints satisfied by the theory (which depends on the coefficients in the Lagrangian). It is found that one can combine these constraints in 9 different ways to obtain non-trivial theories, each with a different inversion formula.