Twisted tensor products of field algebras

Abstract

Let A be a C*-algebra, h a Hilbert space and C the CAR algebra over h. We construct a twisted tensor product of A by C such that the two factors are not necessarily one in the relative commutant of the other. The resulting C*-algebra may be regarded as a generalized CAR algebra constructed over a suitable Hilbert A-bimodule. As an application, we exhibit a class of fixed-time models where a free Dirac field (giving rise to the C factor) in general is not relatively local to a free scalar field (which yields the A factor). In some of the models, gauge-invariant combinations of the two (not relatively local) fields form a local observable net.