Massive Fields with Arbitrary Integer Spin in Homogeneous Electromagnetic Field

TL;DR

This paper develops a method to derive gauge-invariant Lagrangians for arbitrary integer spin fields interacting with a constant electromagnetic field, using algebraic operator techniques applicable in any space-time dimension.

Contribution

It introduces an algebraic approach to construct gauge-invariant Lagrangians for high-spin fields in external electromagnetic fields, extending previous methods to arbitrary integer spins and general dimensions.

Findings

Derived explicit interaction Lagrangian for massive spin-$s$ particles

Constructed gauge-invariant formulations up to second order in electromagnetic field

Method applicable in any space-time dimension

Abstract

We study the interaction of gauge fields of arbitrary integer spins with the constant electromagnetic field. We reduce the problem of obtaining the gauge-invariant Lagrangian of integer spin fields in the external field to purely algebraic problem of finding a set of operators with certain features using the representation of the high-spin fields in the form of vectors in a pseudo-Hilbert space. We consider such a construction up to the second order in the electromagnetic field strength and also present an explicit form of interaction Lagrangian for a massive particle of spin $s$ in terms of symmetrical tensor fields in linear approximation. The result obtained does not depend on dimensionality of space-time.