Twisted tensor products of field algebras

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Let \mathcal{A} be a C*-algebra, {\boldsymbol h} a Hilbert space, and {\mathcal{C}}_{\boldsymbol h} the CAR algebra over {\boldsymbol h} . We construct a twisted tensor product of \mathcal{A} by {\mathcal{C}}_{\boldsymbol h} 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 \mathcal{A} -bimodule. As an application, we exhibit a class of fixed-time models where a free Dirac field (giving rise to the {\mathcal{C}}_{\boldsymbol h} factor) in general is not relatively local to a free scalar field (which yields the \mathcal{A} factor). In some of the models, gauge-invariant combinations of the two (not relatively local) fields form a local observable net.