Interactions of Massive Integer-Spin Fields

TL;DR

This paper reviews gauge-invariant interactions of massive integer-spin fields with electromagnetic and Einstein spaces, providing algebraic methods applicable in arbitrary dimensions.

Contribution

It introduces an algebraic framework for constructing gauge-invariant Lagrangians of higher-spin fields in external backgrounds, extending previous approaches.

Findings

Constructed gauge-invariant Lagrangians up to second order in electromagnetic fields.

Developed a linear approximation framework for Einstein spaces.

Applicable to arbitrary space-time dimensions.

Abstract

We review the interactions of massive fields of arbitrary integer spins with the constant electromagnetic field and symmetrical Einstein space in the gauge invariant framework. The problem of obtaining the gauge-invariant Lagrangians of integer spin fields in an external field is reduced to purely algebraic problem of finding a set of operators with certain features using the representation of the higher-spin fields in the form of vectors in a pseudo-Hilbert space. Such a construction is considered up to the second order for the electromagnetic field and at linear approximation for symmetrical Einstein space. The results obtained are valid for space-time of arbitrary dimensionality.