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

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.

arXiv comment26 pages, additional results, special emphasis on results from Hilbert space positivity which go beyond indefinite metric gauge theory

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