On higher spin interactions with matter

TL;DR

This paper explores the interactions between a scalar field and an infinite tower of higher spin gauge fields, deriving explicit cubic vertices, gauge symmetries, and scattering amplitudes, revealing both high-energy suppression and low-energy dominance of low-spin exchanges.

Contribution

It provides a systematic construction of cubic couplings, conserved currents, and scattering amplitudes for higher spin fields interacting with matter, including exact summation over an infinite tower.

Findings

Explicit form of cubic vertices using Weyl's symbols

Calculation of non-Abelian gauge symmetry group

Total scattering amplitude exhibits exponential fall-off at high energy

Abstract

Cubic couplings between a complex scalar field and a tower of symmetric tensor gauge fields of all ranks are investigated. A symmetric conserved current, bilinear in the scalar field and containing r derivatives, is provided for any rank r>0 and is related to the corresponding rigid symmetry of Klein-Gordon's Lagrangian. Following Noether's method, the tensor gauge fields interact with the scalar field via minimal coupling to the conserved currents. The corresponding cubic vertex is written in a compact form by making use of Weyl's symbols. This enables the explicit computation of the non-Abelian gauge symmetry group, the current-current interaction between scalar particles mediated by any gauge field and the corresponding four-scalar elastic scattering tree amplitude. The exact summation of these amplitudes for an infinite tower of gauge fields is possible and several examples for a definite choice of the coupling constants are provided where the total amplitude exhibits fast (e.g. exponential) fall-off in the high-energy limit. Nevertheless, the long range interaction potential is dominated by the exchange of low-spin particles in the low-energy limit.