Some covariant representations of massless boson fields

by L. Polley, G. Reents and R. F. Streater

Jour. Phys., A14, 2479-2488, 1981.

ABSTRACT

Consider the C*-algebra of the canonical commutation relations (CCR) acted on by a group G of one-particle symmetry transformations V. A symplectic operator T defines a representation pi_T=pi_F\circ T, where pi_F is the Fock representation. The automorphisms of the CCR algebra that are induced by G are shown to be continuously implemented in pi_T if and only if A-V(g)AV^*(g) is a continuous Hilbert-Schmidt 1-cocycle of G; here, A is related to T by T=exp A, A being a suitable bounded, antilinear self-adjoint operator.

Some new examples of fully Poincaré-covariant representations of massless boson fields in 1+1 dimensions are constructed.

REMARK

This paper was the putting together of work done by Polley and me, and some simultaneous work being done by Reents. I did not meet Reents until later; the paper was completed by post, before I had met one of my co-authors!.