The Charge Quantum Numbers of Gauge Invariant Quasi-free Endomorphisms

Details The Charge Quantum Numbers of Gauge Invariant Quasi-free Endomorphisms The Charge Quantum Numbers of Gauge Invariant Quasi-free Endomorphisms

1999-04-22

arxiv.org/abs/math/9904127v1

Mathematics

Operator Algebras

15 pages, no figures

Scientific paper

10.1142/S0129055X00000484

The representations of a group of gauge automorphisms of the canonical commutation or anticommutation relations which appear on the Hilbert spaces of isometries H_\rho implementing quasi-free endomorphisms \rho on Fock space are studied. Such a representation, which characterizes the "charge" of \rho in local quantum field theory, is determined by the Fock space structure of H_\rho itself: Together with a "basic" representation of the group, all higher symmetric or antisymmetric tensor powers thereof also appear. Hence \rho is reducible unless it is an automorphism. It is further shown by the example of the massless Dirac field in two dimensions that localization and implementability of quasi-free endomorphisms are compatible with each other.

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