H. Grosse
Quasifree Second Quantization and Its Relation to Noncommutative Geometry
The paper is published: in J. Lukierski et al. (eds.) "Proc. of the Karpacz School 1994" Kluwer Acad. Publ. (1994) 517-524

MSC:

46L87 Noncommutative differential geometry, See also {58B30,

46L60 Applications of selfadjoint operator algebras to physics, See also {46N50, 46N55, 47D45, 81T05, 82B10, 82C10}

58B30 Noncommutative differential geometry and topology, See also {46L30, 46L87, 46L89}

Abstract: Schwinger terms of current algebra can be identified with nontrivial
cyclic cocycles of a Fredholm module. We discuss its temperature
dependence. Similar anomalies may occur also in spin systems. In simple
examples already an operator--valued cocycle shows up.

Keywords: current algebra, cyclic cocycles of a Fredholm module, spin systems, operator-valued cocycle