Abstract:
This Report consists of two parts; In Part I - Classical theory the author gives the essentials of the theory of non-abelian vector gauge fields. For studying the gauge variance of the theory, the method of functional Lagrange multipliers is introduced. In part II the author deals with Quantum Theory, Starts with the continuation of the discussion of 'formalism with Lagrange Multipliers'. After defining true variables the author introduces gauge transformations in Quantum Field Theory using functional integration method. Both infinitesimal and finite gauge transformations of generating functional for non-abelian gauge vector fields are introduced. The lectures are completed by the discussion about the equivalence of gauges. The author has omitted many important results in the theory of non-abelian fields and the considerations have not been extended to the theory of gravitation. In part II there are some partly original results of the author, like the gauge transformations of the third kind, for non-abelian gauge field, the definition of the true variables, or discussion about the equivalence of gauge. The functional integration here is defined only as a formal operation, using the Feynman integrals assuming their existence and possibility of performing three operations on them, listed in Symanzik's paper.
