Concept and properties of lattice gauge theory

Abstract

A finite lattice in four dimensions and correlation functions defined by integrals are used to formulate quantum gauge theory. Former results on Schwinger-Dyson equations and Ward-Takahashi identities are extended and the much richer structure of quantities and relations, which arises necessarily on the lattice, is discussed. The mechanism of gauge fixing is analyzed and various consequences of this analysis are pointed out. The implications of the generalized fermion degeneracy regularization for the position-space propagator and in the relations for the various currents are shown. An explicit solution for open boundaries is presented and compared with that of the case of the otherwise-used periodic conditions. The analog of continuum methods for dynamical masses and particular decompositions of the fermion determinants are considered. The connection between degeneracy regularization and axial-vector anomaly and the situation for weak interactions are discussed. Further, a number of important details are clarified.