Nonlinear Realization of the General Covariance Group Revisited

TL;DR

This paper introduces a new method for constructing nonlinear realizations of the general covariance group, leading to Einstein-Cartan gravity without decomposing the symmetry group.

Contribution

It presents a modified algorithm that maintains finite dimensionality of the coset manifold by using an infinite vacuum stability group, avoiding subgroup decomposition.

Findings

Successfully derives Einstein-Cartan gravity from the nonlinear realization

Provides a finite-dimensional coset manifold construction

Avoids the need for symmetry group decomposition

Abstract

A modified algorithm for the construction of nonlinear realizations (sigma models) is applied to the general covariance group. Our method features finite dimensionality of the coset manifold by letting the vacuum stability group be infinite. No decomposition of the symmetry group to its finite-dimensional subgroups is required. The expected result, i.e. Einstein-Cartan gravity, is finally obtained.