Spinor and scalar effective actions in gauge-theories

In this dissertation, I investigate the effective action in gauge theories. I present new relations between the spinor and scalar one-loop effective action in constant electromagnetic background fields. I apply similar techniques to show a new correspondence between the spinor and scalar one-loop effective action in curved spacetime. Functional determinants are related to the effective action. I study how some recently developed techniques for calculating functional determinants on radially symmetric backgrounds may be applied to different problems in spinor gauge theories. There are only a few known closed-form results for the effective action at the two-loop level. I present a closed-form for the weak-field expansion coefficients of the two-loop Euler-Heisenberg effective action on a magnetic or electric field.