Nevena Ilieva, Heide Narnhofer
A Fermi Field Algebra as Crossed Product
The paper is published: in: "Sitzungsber., Abt. II, Oesterr. Akad. Wiss., Math.-Naturwiss. Kl. 205 (1997) 13-33

MSC:

46N50 Applications in quantum physics

81T05 Axiomatic quantum field theory; operator algebras

81T40 Two-dimensional field theories, conformal field theories, etc.

Abstract: On the example of Luttinger model and Schwinger model we consider the
observable algebra of interacting fermi systems in two--dimensional
space--time and construct field algebra related to it as a crossed product
with some automorphism group. Fermi statistics results for conveniently
chosen automorphisms. The extension of time evolution to the field algebra
and its asymptotic behaviour are treated. For the Luttinger model time
evolution is asymptotically anticommutative, while for the Schwinger model
we find a reformulation of confinement.

Keywords: Luttinger model, Schwinger model, field algebra, time evolution