A Hilbert space setting for interacting higher spin fields and the Higgs issue

TL;DR

This paper explores a new Hilbert space framework for higher spin fields that employs string-like localization, leading to renormalizable interactions and offering fresh insights into the Higgs mechanism and gauge theories.

Contribution

It introduces a Hilbert space formulation with string-like localization for higher spin fields, enabling renormalizable interactions and providing new perspectives on the Higgs issue.

Findings

String-like localization reduces short distance dimension to d=1 for integer spins.

Renormalizable couplings exist for any spin within this framework.

New conceptual understanding of massless limits and the Higgs mechanism.

Abstract

Wigner's famous 1939 classification of positive energy representations, combined with the more recent modular localization principle, has led to a significant conceptual and computational extension of renormalized perturbation theory to interactions involving fields of higher spin. Traditionally the clash between pointlike localization and the the Hilbert space was resolved by passing to a Krein space setting which resulted in the well-known BRST gauge formulation. Recently it turned out that maintaining a Hilbert space formulation for interacting higher spin fields requires a weakening of localization from point- to string-like fields for which the d=s+1 short distance scaling dimension for integer spins is reduced to d=1 and and renormalizable couplings in the sense of power-counting exist for any spin. This new setting leads to a significant conceptual change of the relation of massless couplings with their massless counterpart. Whereas e.g. the renormalizable interactions of s=1 massive vectormesons with s<1 matter falls within the standard field-particle setting, their zero mass limits lead to much less understood phenomena as "infraparticles" and gluon/quark confinement. It is not surprising that such drastic conceptual changes in the area of gauge theories also lead to a radical change concerning the Higgs issue.