A Hilbert Space setting for higher spin interactions which replaces Gauge Theory

TL;DR

This paper introduces a Hilbert space framework for higher spin interactions that replaces traditional gauge theory, revealing new topological and confinement-related properties through string-localized fields.

Contribution

It develops a Hilbert space approach for higher spin fields, replacing gauge theory, and uncovers novel topological and confinement features.

Findings

Hilbert space positivity yields new topological properties

String-localized fields induce Mexican hat potentials

Potential role of string-localization in confinement

Abstract

The recently discovered Hilbert space description of renormalizable interactions of higher spin (equal or bigger than 1) fields requires to replace the pointlocal s=1 vectorpotentials of indefinite metric (Krein space) BRST gauge theory by their stringlike counterpart in Hilbert space. It is shown that the Hilbert space positivity leads to new properties outside the conceptual range of the gauge theoretic description: topological aspects of Wilson loops, induced normalization terms (in particular Mexican hat type potentials for massive vectormesons coupled to Hermitian scalar field) and a possible role of string-localization in confinerment.