#### Date of Award

1985

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy

#### Abstract

The technique of path integration is remarkably well suited for the calculation of scattering amplitudes in relativistic quantum field theories. However, for the case of a field theory which is defined by a Lagrangian density that is invariant under a set of local gauge transformations, the standard Feynman Path Integral is not adequate for the purpose of performing calculations. This inadequacy arises from a problem of multiple counting since equivalent field configurations, which can be connected by a gauge transformation, are considered to be unique and different when the functional integration is performed. The solution to this problem, which maintains the unitarity of the S matrix, involves restricting the functional integration so that only the physical degrees of freedom can contribute to the path integral at each spacetime point.;The major content of this thesis involves a study, in quantum electrodynamics, of connected Green's Functions Involving Gauge Transformed Field Variables. This is accomplished by including the contributions of the unphysical degrees of freedom, which are associated with the gauge transformation function, in the path integral. There are extra diagrams which contribute to this type of connected Green's function, in addition to those which arise when the corresponding connected Green's function involving the untransformed field variables is considered. The occurrence of these extra diagrams indicates that the term in the gauge field momentum space propagator which is proportional to the tensor ((alpha)-1)p(,(mu))p(,(nu)) can be associated with the propagation of the field associated with the gauge transformation function. The propagation of the physical gauge field does not give rise to any unphysical effects. These arise entirely from the propagation of the unphysical group transformation field.;In addition to the work discussed in the main part of this thesis, several other research problems are studied. Pre-Regularization For Supersymmetry, a technique which allows the WTST identities to be explicitly upheld regardless of the regulating techniques used, is discussed in Appendix 1. The Longitudinal Contributions to the Vacuum Polarization in the 't Hooft-Veltman Gauge are discussed in Appendix 2 and a calculation of The Four Point Function in N = 4 Supersymmetry is presented in Appendix 3.

#### Recommended Citation

Phillips, Stephen Blair, "Green's Functions Involving Gauge Transformed Field Variables" (1985). *Digitized Theses*. 1463.

https://ir.lib.uwo.ca/digitizedtheses/1463