nLab
quasi-free quantum state

Contents

Context

Algebraic Quantum Field Theory

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

In quantum field theory a quantum state is called quasi-free if

  1. its n-point functions are non-vanishing only for even nn;

  2. its 2-point function determines all its nn-point functions.

This reflects the structure of the Wick algebra of quantum observables for the free field.

Examples

References

  • Marek Radzikowski, p. 4 of Micro-local approach to the Hadamard condition in quantum field theory on curved space-time, Commun. Math. Phys. 179 (1996), 529–553 (Euclid)

  • Igor Khavkine, Valter Moretti, section 2.4 of 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 (arXiv:1412.5945)

Last revised on August 5, 2017 at 11:02:24. See the history of this page for a list of all contributions to it.