abstract

Arguments supporting the existence and clarifying the physical interpretation of phase transitions in SU(\(N \to \infty \)) lattice gauge theories are reviewed.

abstract

The aim of these lectures is to present a description of dynamical symmetry breaking that closely parallels spontaneous symmetry breaking via scalar fields. The link is provided by the effective potential that can be defined whether or not elementary scalar fields are present in the theory. I wish to show that the effective potential is calculable in a non-trivial approximation to a gauge theory.

abstract

The relativistic wave equations describing the propagation of isentropic sound waves for an isotropic, ideal fluid moving with an arbitrary fluid velocity are derived. The Green’s functions are given in closed analytic form, and for supersonic flow we find that there is a Mach cone. In the Walecka model of infinite nuclear matter, these sound waves are the elementary excitations of the system and the speed of sound can be calculated explicitly. Finally, we present a possible application to heavy-ion fission induced by an exactly central collision based upon a Cherenkov radiation mechanism.

abstract

It is argued that the electron charge \(e\) and the charge \(e^{\prime }\) of the longitudinal electro-magnetic field are commensurate. The argument is based on the same elementary ideas which lead to the Dirac relation between the charge \(e\) and the magnetic charge \(g\).

abstract

A hypothesis of the “relation-continuum” \(C_4\) is put forward, closely connected with isolation of physical systems, which extends to finite universal constant c the absolute nature of the Galilean relative coordinates and the absolute Newtonian time. Points of \(C_4\) continuum are directly unobservable and the relativistic symmetry \(L_4\) of directly observable space-time events becomes the limiting case of the \(C_4\)-symmetry. Consequently, though the possibility of the hypothesis of \(C_4\)-continuum is due to quantum physics, the modifications it implies come with finite universal constant \(\hslash /c\) and concern the description of the internal structure of bound states only. The \(C_4\)-symmetry of relations, as weaker than the Lorentz-Poincaré \(L_4\)-symmetry of events, makes “more room” for quantum dynamical models. The Feynman graphs phenomenology with form factors (vertex functions) of non-point particles left for experimental determination can be connected with the \(C_4\)-framework which determines their analytic structure. The \(C_4\)-effects then would reveal themselves only in these processes in which composite particles participate. Therefore, the “good” quantum electrodynamics of point-particles is left unmodified. Two off-mass-shell effects are analyzed in the relatively low-energy processes which are connected with the mass-dependent localization of the centre-of-mass of composite particle “\(M\)”. They seem to be crucial for the hypothesis itself.