nLab
Alfsen-Shultz theorem

Context

Functional analysis

Algebraic Quantum Field Theory

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

Introduction

Concepts

field theory: classical, pre-quantum, quantum, perturbative quantum

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

Contents

Idea

The theorem of (Alfsen-Shultz 78) says that two C*-algebras have isomorphic state spaces precisely if as Jordan algebras they are isomorphic.

This is to some extent a Jordan algebra-analog of the Gelfand-Naimark theorem.

Other theorems about the foundations and interpretation of quantum mechanics include:

References

See also

  • Frederic Shultz, Dual maps of Jordan homomorphisms and ∗-homomorphisms between C *C^\ast-algebras, Pacific J. Math. Volume 93, Number 2 (1981), 435-441 (Euclid)

Last revised on December 23, 2017 at 15:45:57. See the history of this page for a list of all contributions to it.