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Stack, John D. Acquarelli, Robert Anthony 2012-05-18T18:16:53Z 2012-05-18T18:16:53Z 10000-01-01 1999 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. Submitted by Elizabeth Kent (eckent2@illinois.edu) on 2012-05-18T18:16:53Z No. of bitstreams: 1 1999_Acquarelli.pdf: 2786304 bytes, checksum: 363930c2155de22d8a4df94c26cc841f (MD5) Made available in DSpace on 2012-05-18T18:16:53Z (GMT). No. of bitstreams: 1 1999_Acquarelli.pdf: 2786304 bytes, checksum: 363930c2155de22d8a4df94c26cc841f (MD5) Previous issue date: 1999 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Elizabeth Kent (eckent2@illinois.edu) on 2012-05-18T18:16:53Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:34:56-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: thesis thesis U of I Only 4255837 http://hdl.handle.net/2142/30866 en ©1999 Robert Anthony Acquarelli instanton Yang-Mills theory The effects of instantons in a finite temperature quantum field theory Dissertation / Thesis text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.