Rich gauge structures from an unitary approach of some massless gauge fields of spins one and two

TL;DR

This paper analyzes massless gauge fields of spins one and two using a unitary approach, performing Dirac analysis on a bosonic form-valued field to classify degrees of freedom and gauge transformations, and constructing first-order Lagrangians.

Contribution

It introduces a systematic Dirac analysis for a bosonic form-valued field with second-order dynamics, classifies parameter-dependent gauge structures, and constructs corresponding first-order Lagrangians.

Findings

Partition of parameter space into seven regions with distinct gauge structures

Explicit determination of degrees of freedom and gauge transformations in each region

Construction of first-order Lagrangians using auxiliary gauge/matter fields

Abstract

Considering a bosonic ($1$-)form-valued $k$-form with a second-order Lagrangian dynamics [depending on two arbitrary real constants] we firstly perform the Dirac analysis. The procedure implies a partition of cardinally seven for the plane of the real parameters that label the starting Lagrangian. In each of the seven partition's components one determines the number and the nature of independent degrees of freedom and also a generating set of gauge transformations. Secondly, with the help of some auxiliary gauge/matter tensor gauge fields, in each of the seven situations, we construct the first-order Lagrangian density corresponding to the second-order one.