Retrieving Yang--Mills--Higgs fields in Minkowski space from active local measurements

TL;DR

This paper demonstrates the recovery of Yang--Mills potentials and Higgs fields in Minkowski space from active measurements, leveraging wave interactions and non-linear effects, with implications for the Standard Model.

Contribution

It introduces a method to reconstruct gauge fields and Higgs fields from source-to-solution data, utilizing non-linear wave interactions in a Minkowski setting.

Findings

Successful reconstruction of Yang--Mills potential and Higgs field from data

Applicable to Standard Model gauge groups

Utilizes non-linear wave interactions for recovery

Abstract

We show that we can retrieve a Yang--Mills potential and a Higgs field (up to gauge) from source-to-solution type data associated with the classical Yang--Mills--Higgs equations in Minkowski space $\mathbb{R}^{1+3}$. We impose natural non-degeneracy conditions on the representation for the Higgs field and on the Lie algebra of the structure group which are satisfied for the case of the Standard Model. Our approach exploits the non-linear interaction of waves generated by sources with values in the centre of the Lie algebra showing that abelian components can be used effectively to recover the Higgs field.