# On the gauge fixing in the Hamiltonian analysis of general teleparallel theories

## TL;DR

This paper demonstrates that fixing the gauge to set the spin connection to zero in teleparallel gravity theories does not alter the degrees of freedom count, ensuring consistent Hamiltonian analysis.

## Contribution

It proves that gauge fixing the spin connection in teleparallel theories does not impact the Hamiltonian degrees of freedom counting.

## Key findings

- Gauge fixing to zero spin connection does not change degrees of freedom.
- Moment of Lorentz transformations are fully determined by tetrad momenta.
- Hamiltonian analysis remains consistent under this gauge choice.

## Abstract

The covariant formulation of teleparallel gravity theories must include the spin connection, which has 6 degrees of freedom. One can, however, always choose a gauge such that the spin connection is put to zero. In principle this gauge may affect counting of degrees of freedom in the Hamiltonian analysis. We show for general teleparallel theories of gravity, that fixing the gauge such that the spin connection vanishes in fact does not affect the counting of degrees of freedom. This manifests in the fact that the momenta of the Lorentz transformations which generate the spin connection are fully determined by the momenta of the tetrads.