Schwinger-Fronsdal Theory of Abelian Tensor Gauge Fields

TL;DR

This paper reviews the Schwinger-Fronsdal theory for Abelian tensor gauge fields, emphasizing its unique current conservation condition that ensures unitarity and describes transverse wave propagation.

Contribution

It clarifies the self-consistency of the theory with traceless current divergence and proposes an equivalent action representation.

Findings

Weaker current conservation suffices for unitarity.

Only transverse polarizations propagate far from sources.

The theory's conditions relate to the existence of certain currents.

Abstract

This review is devoted to the Schwinger and Fronsdal theory of Abelian tensor gauge fields. The theory describes the propagation of free massless gauge bosons of integer helicities and their interaction with external currents. Self-consistency of its equations requires only the traceless part of the current divergence to vanish. The essence of the theory is given by the fact that this weaker current conservation is enough to guarantee the unitarity of the theory. Physically this means that only waves with transverse polarizations are propagating very far from the sources. The question whether such currents exist should be answered by a fully interacting theory. We also suggest an equivalent representation of the corresponding action.