Classical gauge theory
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Date
2015-06-29
Authors
Janse van Rensburg, Richard Wilhelm
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Abstract
This Dissertation presents a systematic study of classical gauge
fie ld theories generated by Lie Groups. I t is based on an action
princfple In which the Lagrangian is required to transform as
invariant under the action of a Lie Group. This leads to a set
of Invariance Id en tities which the functional derivatives of the
Lagrangian must sa tisfy . These id e n titie s, together with the
equations of motion, y ield conservation laws and reveal the
structure of the theory without ex p lic it knowledge of the Lagrangian.
Theories derived In th is way are extremely general and a prescription
for constructing simpler,m1n1mally coupled Lagrangians by the use
of the 4 variance Id en tities Is given.
The work deals separately with an arbitrary Internal group and
with the Poincare Group but draws many p arallels between them.
The Poincare Group Is intimately related to gravity and allows
a general theory to be formulated In which I t Is possible to
discern clearly the roles of the curvature and torsion. I t also
transpires th at certain constraints (or a special choice o f
Lagrangian) must be Imposed to ensure the conservation o f the
gravitational stress tensors. Finally, a number of specific
theories which naturally suggest themselves are analysed In terms
of the general theory.
Description
A Dissertation Submitted to the Faculty of Science
University of the Witwatersrand, Johannesburg
In Partial Fulfilment of the Requirements of the
Degree of Master of Science
Johannesburg 1881