Gauge bosons at zero and finite temperature

TL;DR

This paper discusses gauge fixing in non-Abelian gauge theories, especially Yang-Mills theories, addressing the Gribov-Singer ambiguity, and explores the properties of gauge bosons at various temperatures using correlation functions.

Contribution

It introduces a gauge-fixing prescription that resolves the Gribov-Singer ambiguity and applies it to analyze gauge bosons beyond perturbation theory in different dimensions and gauge algebras.

Findings

Gauge bosons lack on-shell mass poles at all energy scales.

Finite temperature effects reflect the phase structure of Yang-Mills theory.

The phase transition does not deconfine gauge bosons, despite Stefan-Boltzmann thermodynamics.

Abstract

Gauge theories of the Yang-Mills type are the single most important building block of the standard model and beyond. Since Yang-Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Beyond perturbation theory, gauge-fixing in non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity. The construction and implementation of a method-independent gauge-fixing prescription to resolve this ambiguity is the most important step to describe gauge bosons beyond perturbation theory. Proposals for such a procedure, generalizing the perturbative Landau gauge, are described here. Their implementation are discussed for two example methods, lattice gauge theory and the quantum equations of motion. The most direct access to the properties of the gauge bosons is provided by their correlation functions. The corresponding two- and three-point correlation functions are presented at all energy scales. These give access to the properties of the gauge bosons, like their absence from the asymptotic physical state space, the absence of an on-shell mass pole, particle-like properties at high energies, and their running couplings. Furthermore, auxiliary degrees of freedom are introduced during gauge-fixing, and their properties are discussed as well. These results are presented for two, three, and four dimensions, and for various gauge algebras. Finally, the modifications of the properties of gauge bosons at finite temperature are presented. Evidence is provided that these reflect the phase structure of Yang-Mills theory. However, it is found that the phase transition is not deconfining the gauge bosons, although the bulk thermodynamical behavior is of a Stefan-Boltzmann type. The resolution of this apparent contradiction is also presented. This resolution also provides an explicit and constructive solution to the Linde problem.