The Higgs mechanism in nonlocal field theory

TL;DR

This paper demonstrates that a nonlocal scalar electrodynamics model can replicate the Higgs mechanism's success in local theories, maintaining the same solutions and degrees of freedom while achieving super-renormalizability.

Contribution

It introduces a nonlocal field theory framework that preserves the Higgs mechanism's features and ensures super-renormalizability, extending the understanding of nonlocal quantum field theories.

Findings

Same Higgs mechanism applies in nonlocal theory

Perturbative degrees of freedom are preserved

The theory is super-renormalizable or finite at quantum level

Abstract

We provide an example of nonlocal scalar electrodynamics that allows the same Higgs mechanism so successful in local field theory. The nonlocal action is structured in order to have the same exact solutions and the same equations of motion for perturbations of the local theory, at any perturbative order. Therefore, the perturbative degrees of freedom that propagate in the unstable vacuum are reshuffled when the stable vacuum is replaced in the EoM, but their number does not change at any perturbative order, and their properties are the same like in the usual local theory. Finally, the theory is super-renormalizable or finite at quantum level.