Lorentz covariance and kinetic charge

by P. Basarab-Horwath R. F. Streater and Jill Wright

ABSTRACT

There is a one-to-one correspondence between inequivalent covariant displaced Fock representations of the free relativistic field and the 1-cohomology of the Poincaré group with coefficients in the one-particle space.

Representations with positive energy are obtained from cocycles with finite energy; these new representations have particle-like properties and are interpreted as condensed states of matter without a sharply defined mass.

The 1-cohomology groups of the restricted Poincaré group are calculated. These are trivial in 3- or 4-dimensional space-time, or if the mass is non-zero. Non-trivial cocycles for subgroups lead to representations in which P-invariance is spontaneously broken. We recover P-invariance in a direct integral representation possessing a gauge group, and a superselection structure labelled by the velocities of the condensed states of matter which are the cocycles determining each irreducible component of the representation. A model in 4-dimensional space-time is constructed.