nLab
star-representation

Contents

Context

Representation 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

Contents

Idea

For (𝒜,*)(\mathcal{A}, \ast) a star-algebra and \mathcal{H} a Hilbert space, a star-representation of (𝒜,*)(\mathcal{A},\ast) on \mathcal{H} is a homomorphism of star algebras from 𝒜\mathcal{A} to linear operators on (a dense subspace of) \mathcal{H}.

References

  • Igor Khavkine, Valter Moretti, def. 7 in Algebraic QFT in Curved Spacetime and quasifree Hadamard states: an introduction, Chapter 5 in Romeo Brunetti et al. (eds.) Advances in Algebraic Quantum Field Theory, , Springer, 2015

Last revised on December 3, 2017 at 16:29:23. See the history of this page for a list of all contributions to it.