Date of Award


Degree Type


Degree Name

Doctor of Philosophy


In the past few years a new method of regularization, called operator regularization (o.r.), has been developed to regulate formal divergences that arise in quantum field theory. This technique is characterized by the fact that no divergent quantities ever arise once the technique is applied, even after the regulating parameter approaches its limiting value, and that under certain conditions the symmetries present in the initial Lagrangian are not explicitly broken. The technique is developed in more detail for beyond one-loop order in perturbation theory, and some two-loop calculations in o.r. are done for the first time. First, the Schwinger expansion, which finds a natural setting in o.r., is used to calculate the general (off-diagonal) coefficients of the DeWitt expansion, which makes it possible to use this expansion beyond one-loop order. An approach to calculating renormalization group functions based on examining finite Green functions is then presented, and explicit calculations of the renormalization group functions to two-loop order are performed in scalar {dollar}\phi\sbsp{lcub}6{rcub}{lcub}3{rcub}{dollar} and {dollar}\phi\sbsp{lcub}4{rcub}{lcub}4{rcub}{dollar} models using the newly-derived DeWitt expansion coefficients. Two other applications are presented. One is the computation of the divergence of the U(1) axial current in the presence of constant U(1) and SO(3) gauge fields to two-loop order. This combines o.r. with a functional technique, and a result compatible with the Adler-Bardeen result is obtained. The last application of o.r. is to massive Yang-Mills theory. Introducing a mass breaks gauge invariance and makes the theory non-renormalizable. However, since o.r. always gives finite results, we have here an opportunity to examine a non-renormalizable theory without the usual difficulties. It turns out that the arbitrary mass scale parameter {dollar}\mu\sp2{dollar} loses it arbitrariness and becomes fixed (experimentally) by the strength of a radiatively induced four-point interaction.



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