Higgs and gravitational scalar fields together induce Weyl gauge

TL;DR

This paper explores how Higgs and scalar fields, coupled with gravity in a scale-invariant framework, induce a Weyl gauge condition that links electroweak theory and gravity, affecting atomic frequency interpretations.

Contribution

It introduces a unified approach combining Higgs and scalar fields with gravity in a Weyl geometric setting, providing new insights into scale symmetry and gauge fixing.

Findings

Existence of a common ground state for Higgs and scalar fields.

Coupling of scalar fields to scalar curvature in Weyl geometry.

Reinterpretation of Weyl gauge as a combined electroweak and gravitational effect.

Abstract

A common biquadratic potential for the Higgs field $h$ and an additional scalar field $\phi$, non minimally coupled to gravity, is considered in locally scale symmetric approaches to standard model fields in curved spacetime. A common ground state of the two scalar fields exists and couples both fields to gravity, more precisely to scalar curvature $R$. In Einstein gauge ($\phi = const$, often called "Einstein frame"), also $R$ is scaled to a constant. This condition makes perfect sense, even in the general case, in the Weyl geometric approach. There it has been called {\em Weyl gauge}, because it was first considered by Weyl in the different context of his original scale geometric theory of gravity of 1918. Now it seems to get new meaning as a combined effect of electroweak theory and gravity, and their common influence on atomic frequencies.