Spin and orbital angular momentum of the tensor gauge field

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.