The effects of instantons in a finite temperature quantum field theory
Acquarelli, Robert Anthony
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/30866
Description
Title
The effects of instantons in a finite temperature quantum field theory
Author(s)
Acquarelli, Robert Anthony
Issue Date
1999
Doctoral Committee Chair(s)
Stack, John D.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
instanton
Yang-Mills theory
Language
en
Abstract
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.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
