Kazuyasu Shigemoto

Collective Excitations in Local-Gauge Invariant Superconductivity Models

We consider a system which is described by a Lagrangian of Heisenherg-Nambu-JonaLasinio type and also has local gauge invariances. It is shown that collective excitations of fermion-antifermion pair could occur in scalar and ps-scalar channels, but not in vector or axial-vector channels. This is proved, as an example, in a course of derivation of the Weinberg-Salam model from the above type Lagrangian.

Shock Waves in Collective Field Theories for Many Particle Systems

The study of collective motion in many body systems was one of the active subjects of the 1950s.n Recently Jevicki and Sakita 2) have considered this old subject in order to explore and motivate applications of similar ideas and methods to modern problems of quantum field theory. Their collective field approach to many particle quantum mechanical systems is elegant and sufficiently general so that one can apply the formalism to quantum field theories including non-Abelian gauge theories.

Effective Actions in Lattice Gauge Theories

Effective coupling constants of non-Abelian lattice gauge theories are calculated when actions on each cell are small. The recursion equation for the effective coupling constant 9err(t) shows that Qerr(t) increases exponentially in the infrared region. This behavior is also obtained from the law of area due to Wilson. An existence of fixed points in QED is also suggested. In our opinion there have so far been no methods appropriate for the estimation. Migdals recursion equation can be numerically solved only on a computer, even in the strong coupling region. We propose here a simple recursion formula for the effective coupling constant, which is easily derived by analytic methods and is valid well in the strong coupling region. Our investigation is unsatisfactory in the sense that it cannot say anything about the asymptotic freedom in the ultraviolet region, but in the infrared region our formula will be quite satisfactory. First we derive in § 2 the effective coupling formula from the direct calculation of the effective action. In § 3 this formula is shown to be derived also from the law of area. An existence of fixed points in QED is also suggested.