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Gauge theories in three dimensions


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Waites, Anthony Brian 1994 , 'Gauge theories in three dimensions', PhD thesis, University of Tasmania.

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Field theories in 2+ 1 space-time dimensions are of interest both intrinsically, due
to their novel properties such as actions which are topologically non-trivial, and
also due to their ability to explain of phenomena such as the fractional quantum
Hall effect and certain behaviour of high Tc superconductors, and for their use in
conformal field theory in 2D.
This thesis begins by considering scalar and spinor QED in 2+ 1 dimensions,
performing perturbation theory to study its behaviour (without allowing the presence
or dynamical generation of a parity-violating photon mass). It is found, as
first noted by Jackiw and Templeton, that an IR instability prohibits such a
perturbative study. The gauge technique is adopted as a non-perturbative alternative,
and the photon is allowed to be "dressed" in a cloud of fermion loops,
yielding results which encompass the perturbation results in the UV region, whilst
remaining finite at IR momenta.
Chern-Simons theory is then considered, where the photon is allowed to acquire
a parity-violating mass. In order to use dimensional regularization to handle
the. apparently UV divergent integrals which appear, a new formulation of the
theory is proposed, allowing the action to be written in arbitrary D dimensions,
so that the integrals can be safely evaluated. It is also found that the IR problems
which plague the conventional theory are no longer present, as the photon propagator
behaviour has been "softened" by the photon mass, allowing perturbation
results to be obtained.
Finally, the idea of mass generation within these theories is considered in more
detail, where we see that the presence of a fermion mass will cause a photon mass
to be dynamically generated, and vice versa. These ideas are then generalized for
arbitrary odd dimensional parity-violating theories.

Item Type: Thesis - PhD
Authors/Creators:Waites, Anthony Brian
Keywords: Gauge fields (Physics)
Copyright Holders: The Author
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Copyright 1994 the Author - The University is continuing to endeavour to trace the copyright
owner(s) and in the meantime this item has been reproduced here in good faith. We
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Additional Information:

Includes bibliographical references (p. 95-108). Thesis (Ph.D.)--University of Tasmania, 1994

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