Covariance principle and covariance group in presence of external E.M. Fields

Abstract

The definition of (kinematical) covariance, by means of the properties and the equivalence relations of inertial systems, can give, as is well known, very useful information on the admissible equations of motion and on the group theoretical concept of an elementary particle (which is defined as an irreducible quantum-mechanical system obeying such an equation). Here we consider the case where an external (classical) e.m. field is present. In this talk we show that for such a system, the relativistic covariance operator group is in general no longer homomorphic to the covering group of the Poincaré group (as in the free particle case), but to contain it only as a factor group. This larger covariance group can be derived on the basis of some simple physical assumptions, independently of any equation of motion.

Its (projective unitary-antiunitary) irreducible representations have been all determined and classified. Some conclusions are drawn concerning the properties of the corresponding covariant equations of motion and a group theoretical definition of an elementary particle in interaction with such a field is proposed (The special case of zero field reduces of course to the known results of Wigner). Some aspects of this approach lead to a possible solution of the so-called a-causality troubles for particles with spin equal to or larger than 1.