ASPECTS OF SYMMETRY BEHAVIOR IN QUANTUM FIELD THEORY

Two aspects of symmetry behavior in quantum field theories are explored. The first is the nature of the phase transition which occurs in 4D gauge theories coupled to scalar and spinor fields at finite temperature. It is shown that the critical behavior can be isolated in an effective 3D theory of the zero frequency mode whose Lagrangian is then investigated by (epsilon)-expansion techniques. There follows an investigation of the problems encountered in trying to calculate patterns of dynamical symmetry breaking in lattice gauge theories. The importance of realizing the proper continuum anomaly is emphasized and some calculational procedures are discussed.