Spin and orbital angular momentum of the tensor gauge field

TL;DR

This paper investigates the angular momentum properties of tensor gauge fields, revealing that their angular momentum vanishes in stationary systems and can induce intrinsic interactions affecting Poincaré symmetry.

Contribution

It extends the analysis of gauge field angular momentum from vectors to tensors, uncovering unique features and gauge invariance properties.

Findings

Angular momentum vanishes for stationary tensor gauge fields after gauge fixing.

Angular momentum exhibits one-parameter gauge invariance.

Tensor gauge coupling can induce intrinsic interactions in Poincaré generators.

Abstract

Following the recent studies of the trickiness in spin and orbital angular momentum of the vector gauge fields, we perform here a parallel analysis for the tensor gauge field, which has certain relation to gravitation. Similarly to the vector case, we find a nice feature that after removing all gauge degrees of freedom the angular momentum of the tensor gauge field vanishes for a stationary system. This angular momentum also shows a one-parameter invariance over the infinitely many ways of complete gauge fixing for the tensor field. The tensor gauge coupling, however, does exhibit a critical difference from the vector gauge coupling that it may induce intrinsic interaction terms into the spatial translation and rotation generators, leaving none of the ten Poincar\'e generators interaction-free.