Wigner's little group as a gauge generator in linearized gravity theories

TL;DR

This paper demonstrates that the translational subgroups of Wigner's little group generate gauge transformations in linearized gravity theories across different dimensions, revealing a unified gauge-generating mechanism via dimensional descent.

Contribution

It systematically derives gauge transformations from translational groups in linearized gravity and related theories, establishing a unified framework through dimensional descent.

Findings

Translational groups generate gauge transformations in linearized Einstein gravity.

Representation of T(1) generates gauge transformations in 2+1D Einstein-Chern-Simons theory.

Polarization tensor of Einstein-Pauli-Fierz theory splits into a pair of Einstein-Chern-Simons tensors.

Abstract

We show that the translational subgroup of Wigner's little group for massless particles in 3+1 dimensions generate gauge transformation in linearized Einstein gravity. Similarly a suitable representation of the 1-dimensional translational group T(1) is shown to generate gauge transformation in the linearized Einstein-Chern-Simons theory in 2+1 dimensions. These representations are derived systematically from appropriate representations of translational groups which generate gauge transformations in gauge theories living in spacetime of one higher dimension by the technique of dimensional descent. The unified picture thus obtained is compared with a similar picture available for vector gauge theories in 3+1 and 2+1 dimensions. Finally, the polarization tensor of Einstein-Pauli-Fierz theory in 2+1 dimensions is shown to split into the polarization tensors of a pair of Einstein-Chern-Simons theories with opposite helicities suggesting a doublet structure for Einstein-Pauli-Fierz theory.