A note on higher rank descriptions of massless and massive spin-1 particles

Abstract

The Maxwell theory can be written as a first order model with the help of a two-form auxiliary field, such master action allows the proof of duality between 1-form and D−3 forms. Here we show that the replacement of the two-form auxiliary field by an arbitrary (non symmetric) rank-2 tensor leads to a new massless spin-1 dual theory in terms of a partially antisymmetric rank-3 tensor. In the massive spin-1 case we have a non symmetric generalization of the massive two-form theory (Kalb–Ramond). The coupling of the massive non symmetric spin-1 model to matter fields is investigated via master actions.We also show that massive models with severe discontinuity in their massless limit can also be obtained from Kaluza–Klein dimensional reduction of massless higher rank tensors which become Stueckelberg fields after the reduction.