Schwinger-Fronsdal Theory of Abelian Tensor Gauge Fields

TL;DR

The work analyzes the Schwinger–Fronsdal framework for Abelian tensor gauge fields of rank $s$, showing that a quadratic, double-traceless action yields equations of motion $LA=J$ whose current is only weakly conserved yet still propagates only transverse modes, preserving unitarity. It develops a gauge-fixed solution in de Donder–Fronsdal gauge and a propagator-based analysis of current exchange, demonstrating that, with weak current conservation, the physical content reduces to transverse polarizations and a constructive projection to a conserved effective current. It further provides an alternative, nonlocal geometric representation of the action via generalized field strengths and discusses how to realize a conserved current within this framework. The results clarify the role of current conservation in higher-spin Abelian theories and offer methodological pathways toward interacting constructions with maintained unitarity.

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.