Stueckelberg and Higgs Mechanisms: Frames and Scales

TL;DR

This paper compares the Stueckelberg and Higgs mechanisms for gauge boson mass generation in Yang-Mills theory, linking them to conformal geometry and exploring implications for scale, confinement, and gauge fields.

Contribution

It introduces a geometric framework connecting Higgs fields and coupling parameters with conformal structures on gauge bundle fibers, extending the Stueckelberg mechanism to include Higgs dynamics.

Findings

Stueckelberg field identified as a G-frame on gauge bundle

Higgs fields linked to conformal rescaling of fibers

Running couplings correspond to fiber expansion or contraction

Abstract

We consider Yang-Mills theory with a compact gauge group $G$ on Minkowski space ${\mathbb R}^{3,1}$ and compare the introduction of masses of gauge bosons using the Stueckelberg and Higgs mechanisms. The Stueckelberg field $\phi$ is identified with a $G$-frame on the gauge vector bundle $E$ and the kinetic term for $\phi$ leads to the mass of the gauge bosons. The Stueckelberg mechanism is extended to the Higgs mechanism by adding to the game a scalar field describing rescaling of metric on fibres of $E$. Thus, we associate Higgs fields as well as running coupling parameters with conformal geometry on fibres of gauge bundles. In particular, a running coupling tending to zero or to infinity is equivalent to an unbounded expansion of $G$-fibres or its contraction to a point. We also discuss scale connection, space-time dependent Higgs vacua and compactly supported gauge and quark fields as an attribute of confinement.