Some local covariant representations of the canonical anticommutation relations

by Z. J. Hermaszewski and R. F. Streater.

ABSTRACT

We find some non-Fock representations of the canonical anticommutation relations in 1+1 dimensions. These representations, obtained by a Bogoliubov transformation of the Fock annihilation and creation operators, are Poincaré covariant, have positive energy, and are labelled by two conserved charges which take on continuous values in the interval [0,2\pi).

REMARKS

The currents of the model exhibit an axial anomaly, in that the corresponding gauge transformations commute as automorphisms of the current algebra, but the currents do not commute. The models are local examples of the general class of representations classified in a paper with K. Kraus. Similar examples, but with positive mass, were analysed in work with Gallone, Sparzani and Ubertone.