Interactions with quadratic dependence on string-localized massive vectormesons: massive scalar quantum electrodynamics

TL;DR

This paper explores string-localized interactions of massive vector mesons with scalar matter, revealing new insights into infrared problems, confinement, and renormalizability for higher-spin fields within a Hilbert space framework.

Contribution

It introduces a string-localization approach that preserves Hilbert space positivity, enabling renormalizable interactions for higher-spin fields and relating stringlike and pointlike interactions.

Findings

String-localization improves short-distance behavior of higher-spin fields.

The approach offers a new perspective on infrared problems and confinement.

A local relation between stringlike and pointlike interactions is established.

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 s>1/2. The starting observation was that the well-known clash between point-localized gauge theories and the Hilbert space, which hitherto has been solved by using a Krein space setting, can also be solved by preserving the Hilbert space setting; in this case the theory selects the tightest covariant localization which is consistent with the Hilbert space positivity. The resulting semiinfinite spacelike string-localization for all (m=0,s>1/2) representations does not only lead to a new insight into the origin of infrared problems (including confinement), but also improves the short-distance behavior of massive s>1/2 fields to the extend that the power-counting criterion admits candidates for renormalizable interactions for arbitrary high spins. In this work the new situation is exemplified for the interaction of massive vectormesons with scalar charged- and neutral- (Higgs) matter, for which the new "adiabatic equivalence principle" leads to a local relation between a renormalizable stringlike and a nonrenormalizable (but nevertheless finite-parametric) pointlike interaction.