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A Semi-classical analysis of the Wilson Loop in a 2+1 Dimensional Yang-Mills theory with a monopole gas Clark, Michael Perry
Abstract
In this paper we consider a Wilson loop in a 2+1 dimensional pure Yang-Mills theory with an SU(2) gauge group. The initial goal is to test a conjecture of A. M. Polyakov's which proposes that if one considers the field-strength, Fa„, and the gauge field, Aa, as independent, random variables, then a sum over surfaces spanning the Wilson loop will re-introduce the Bianchi Identity. We do this by introducing an additional functional integral over a sigma model variable which unravels the path-ordering of the loop variables. Then, via a non-Abelian Stokes' theorem, we express the Wilson loop as a surface integral with separate functional integrals over both Fa and Aa. At the semi-classical level, characterized by a large spin parameter, we find that the conjecture holds true - the Bianchi Identity arises as a natural constraint. Secondly, we find that this reformulation of the Wilson loop naturally allows for an arbitrary distribution of monopoles. We treat both the cases of a single monopole and a monopole gas. In the latter case case we demonstrate the confinement of quarks for states of half-odd-integer spin.
Item Metadata
Title |
A Semi-classical analysis of the Wilson Loop in a 2+1 Dimensional Yang-Mills theory with a monopole gas
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1997
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Description |
In this paper we consider a Wilson loop in a 2+1 dimensional pure Yang-Mills theory
with an SU(2) gauge group. The initial goal is to test a conjecture of A. M. Polyakov's
which proposes that if one considers the field-strength, Fa„, and the gauge field, Aa, as
independent, random variables, then a sum over surfaces spanning the Wilson loop will
re-introduce the Bianchi Identity. We do this by introducing an additional functional
integral over a sigma model variable which unravels the path-ordering of the loop variables.
Then, via a non-Abelian Stokes' theorem, we express the Wilson loop as a surface
integral with separate functional integrals over both Fa and Aa. At the semi-classical
level, characterized by a large spin parameter, we find that the conjecture holds true -
the Bianchi Identity arises as a natural constraint.
Secondly, we find that this reformulation of the Wilson loop naturally allows for an
arbitrary distribution of monopoles. We treat both the cases of a single monopole and
a monopole gas. In the latter case case we demonstrate the confinement of quarks for
states of half-odd-integer spin.
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Extent |
3496125 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-03-24
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0085080
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1997-11
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.