Non-Abelian tensor gauge fields: generalization of Yang-Mills theory

TL;DR

This paper extends Yang-Mills theory to include tensor gauge fields, forming a larger gauge group with new invariants, enabling consistent interactions of higher-spin gauge bosons without higher derivatives.

Contribution

It introduces a novel non-Abelian gauge extension incorporating tensor fields and constructs invariant Lagrangians with enhanced gauge symmetry.

Findings

Defines a new large gauge group for tensor fields.

Constructs invariant Lagrangians quadratic in field strengths.

Eliminates negative norm states, resulting in physical tensor gauge bosons.

Abstract

We suggest an extension of the gauge principle which includes tensor gauge fields. The extended non-Abelian gauge transformations of the tensor gauge fields form a new large group. On this group one can define field strength tensors, which are transforming homogeneously with respect to the extended gauge transformations. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of tensor gauge fields of arbitrary large integer spin $1,2,...$. It does not contain higher derivatives of the tensor gauge fields, and all interactions take place through three- and four-particle exchanges with dimensionless coupling constant. In this extension of the Yang-Mills theory the vector gauge boson becomes a member of a bigger family of tensor gauge bosons. We shall present a second invariant Lagrangian which can be constructed in terms of the above field strength tensors. The total Lagrangian is a sum of the two Lagrangians and exhibits enhanced local gauge invariance with double number of gauge parameters. This allows to eliminate all negative norm states of the nonsymmetric second-rank tensor gauge field, which describes therefore three physical polarizations: two symmetric polarizations of helicity-two massless charged tensor gauge bosons and antisymmetric polarization of helicity-zero charged B field.