Algebraic quantum kk-theory

Algebraic K-theory of Fredholm Modules and Kk-theory

Kasparov KK-groups KK(A,B) are represented as homotopy groups of the Pedersen-Weibel nonconnective algebraic K-theory spectrum of the additive category of Fredholm (A,B)-bimodules for A and B, respectively, a separable and σ-unital trivially graded real or complex C∗-algebra acted upon by a fixed compact metrizable group.

Algebraic Quantum Field Theory∗

Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools — the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is...

Algebraic Quantum Theory

We present the mathematical setting of an algebraic approach to quantum theory, including the Tomita–Takesaki theory, liouvilleans and quantum dynamical systems, and non-commutative integration up to the Falcone–Takesaki theory.

Algebraic quantum theory

The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global program based on the infinite dimensional representations of algebraic groups over adele rings. In this context, algebraic quanta, strings and fields of particles ...

Symmetry in algebraic quantum theory