Classical gauge theory

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.