Stueckelberg and Higgs Mechanisms: Frames and Scales

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 $\varphi$ is identified with a $G$-frame on the gauge vector bundle $E$ and the kinetic term for $\varphi$ 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.

arXiv comment22 pages; v3: references added, published version

References in corpus (6)

• The Stueckelberg Field
• Local subsystems in gauge theory and gravity
• Constituent Quarks from QCD
• Bundle geometry of the connection space, covariant Hamiltonian formalism, the problem of boundaries in gauge theories, and the dressing field method
• If the Weak Were Strong and the Strong Were Weak
• A phase of confined electroweak force in the early Universe

Cited by in corpus (1)

• Geometric confinement in gauge theories