The Erwin Schrr Odinger International Institute for Mathematical Physics Quasifree Second Quantization and Its Relation to Noncommutative Geometry Quasifree Second Quantization and Its Relation to Noncommutative Geometry

Quasifree Second Quantization and Its Relation to Noncommutative Geometry

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. Lectures given at the XXX–th Karpacz Winter School in Theoretical Physics, Poland, 1994.

The Erwin Schrr Odinger International Institute for Mathematical Physics Topologically Nontrivial Field Conngurations in Noncommutative Geometry Topologically Nontrivial Field Conngurations in Noncommutative Geometry 1

In the framework of noncommutative geometry we describe spinor elds with nonvanishing winding number on a truncated (fuzzy) sphere. The corresponding eld theory actions conserve all basic symmetries of the standard commutative version (space isometries and global chiral symmetry), but due to the noncommutativity of the space the elds are regularized and they contain only nite number of modes. 2...

The Erwin Schrr Odinger International Institute for Mathematical Physics Noncommutative 3-sphere: a Model of Noncommutative Contact Algebras Noncommutative 3-sphere: a Model of Noncommutative Contact Algebras

The Erwin Schrr Odinger International Institute for Mathematical Physics Noncommutative Lattices and Their Continuum Limits Noncommutative Lattices and Their Continuum Limits

We consider nite approximations of a topological space M by noncommutative lattices of points. These lattices are structure spaces of noncommutative C algebras which in turn approximate the algebra C(M) of continuous functions on M. We show how to recover the space M and the algebra C(M) from a projective system of noncommutative lattices and an inductive system of noncommutative C-algebras, re...

The Erwin Schrr Odinger International Institute for Mathematical Physics K{theory of Noncommutative Lattices K-theory of Noncommutative Lattices

Noncommutative lattices have been recently used as nite topological approximations in quantum physical models. As a rst step in the construction of bundles and characteristic classes over such noncommutative spaces, we shall study their K-theory. We shall do it algebraically, by studying the algebraic K-theory of the associated algebras of`continuous functions' which turn out to be noncommutati...