The effects of instantons in a finite temperature quantum field theory

In this thesis we describe the Euclidean path integral approach and instanton methods for investigating a SU(2) Yang-Mills theory at finite temperature. We first begin with a review of tunneling in a one-dimensional periodic potential. Here we introduce the methods of Euclidean path integrals and the idea of an instanton. Next we proceed to review Yang-Mills' theory at zero temperature. We perform calculations in a dilute instanton gas approximation. We show that in this approximation, instantons increase coupling between the quarks. We then show that the dilute gas approximation is suspect in the zero temperature formalism because divergences occur when trying to include instantons of all sizes in the theory. We then introduce the finite temperature formalism where the dilute gas approximation is valid. Finally, we show that only certain instantons, namely those with a scale parameter of ρ > β, make significant contributions to the inter-quark potential and spatial Wilson Loop in the dilute gas approximation at finite temperature. Finally, we point out the resemblance between these ρ > β instantons and monopoles. Our results are compared with those obtained from simulations and numerical calculations.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2012

Author dc:creator

• Acquarelli, Robert Anthony

Contributors dc:contributor

• Stack, John D.

• instanton
• Yang-Mills theory

Statement dc:rights

• ©1999 Robert Anthony Acquarelli

Language dc:language

en

Identifier

4255837

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/30866