First Order Formalism for Mixed Symmetry Tensor Fields

TL;DR

This paper develops a first order Lagrangian formalism for mixed symmetry tensor fields, resembling tetrad gravity, which simplifies the study of their interactions and provides explicit formulations.

Contribution

It introduces a novel first order Lagrangian approach for mixed symmetry tensor fields, facilitating interaction analysis and drawing parallels with tetrad formalism in gravity.

Findings

Explicit first order Lagrangians for mixed symmetry tensors are derived.

The formalism resembles tetrad gravity, aiding interaction studies.

Examples of interactions for these fields are provided.

Abstract

In this paper we give explicit first order Lagrangian formulation for mixed symmetry tensor fields \Phi_{[\mu\nu],\alpha}, T_{[\mu\nu\alpha],\beta} and R_{[\mu\nu],[\alpha\beta]}. We show that such Lagrangians could be written in a very suggestive form similar to the well known tetrad formalism in gravity. Such description could simplify the investigations of possible interactions for these fields. Some examples of interactions are given.