Hidden diffeos in the Hamiltonian formulation of a background independent field theory

TL;DR

This paper explores the geometric Hamiltonian formulation of a modified background-independent field theory, revealing how 3D diffeomorphisms integrate with gauge symmetries, advancing understanding of its symmetry structure.

Contribution

It demonstrates that 3D diffeomorphisms can be incorporated as gauge transformations in a modified Husain-Kuchař model, highlighting new symmetry aspects.

Findings

3D diffeomorphisms are compatible with gauge transformations

The model maintains connection as a dynamical variable

Geometric analysis clarifies symmetry structure

Abstract

We analyze from a geometric perspective the Hamiltonian formulation of a recent modification of the Husain-Kucha\v{r} model where, while preserving the connection as a dynamical variable, the other field is restricted to be the exterior covariant derivative of a Lie algebra-valued function. We prove that 3-dimensional diffeomorphisms can be accommodated among the local gauge transformations of the model in addition to the internal gauge symmetries.