Date of Award

Fall 1980

Project Type


Program or Major


Degree Name

Doctor of Philosophy


A gauge invariant action functional for non-abelian gauge theories is derived from the vacuum to vacuum transition amplitude. This effective action is then examined in the loop expansion, where it is demonstrated that the unrenormalized one-loop term is equal to the change in the zero point energy of the theory due to the presence of a non-vanishing background field. The one loop term is carefully evaluated in Euclidean space, and the positivity of the one-loop eigenvalues is related to classical stability in terms of energy minimality. The case of negative eigenvalues is considered and a procedure for "regularizing" the one loop term for this problem is defined. An imaginary part of the effective action to this order is shown to indicate an instability of the theory in the presence of a non-vanishing background field. Finally, complications due to the occurrence of "gyroscopic" terms are reviewed.