Massive Fields of Arbitrary Integer Spin in Symmetrical Einstein Space

TL;DR

This paper develops a method to describe gauge fields of any integer spin in symmetrical Einstein spaces, providing explicit Lagrangians and gauge transformations for massive spins 1 and 2.

Contribution

It reduces the problem of constructing gauge-invariant Lagrangians for high-spin fields to an algebraic problem and explicitly formulates interactions in curved backgrounds.

Findings

Derived algebraic conditions for gauge invariance in Einstein spaces

Constructed explicit interaction Lagrangians for spins 1 and 2

Analyzed linear order effects of curvature on high-spin fields

Abstract

We study the propagation of gauge fields with arbitrary integer spins in the symmetrical Einstein space of any dimensionality. We reduce the problem of obtaining a gauge-invariant Lagrangian of integer spin fields in such background to an purely algebraic problem of finding a set of operators with certain features using the representation of high-spin fields in the form of some vectors of pseudo-Hilbert space. We consider such construction in the linear order in the Riemann tensor and scalar curvature and also present an explicit form of interaction Lagrangians and gauge transformations for massive particles with spins 1 and 2 in terms of symmetrical tensor fields.