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continuous field of C*-algebras

Contents

Context

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Operator algebra

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Bundles

Contents

Idea

A continous field of C *C^\ast-algebras is a topological space XX and a C*-algebra A xA_x for each point xX x \in X, such that in some sense these algebras vary continuously as xx varies in XX. Hence it is a kind of topological bundle of C *C^\ast-algebras. It is also an example of a Fell Bundle over XX when XX is thought of as a topological groupoid with only identity morphisms.

Applications

In strict deformation quantization

In C* algebraic deformation quantization continuous fields of C *C^\ast-algebras over subspaces of the standard interval (tyically {1,12,13,,0}[0,1]\{1 , \frac{1}{2}, \frac{1}{3}, \cdots, 0\} \hookrightarrow [0,1]) such that in the limit this becomes a Poisson algebra constitute deformation quantizations of this Poisson algebra.

References

Last revised on February 25, 2014 at 23:05:44. See the history of this page for a list of all contributions to it.