nLab
interacting vacuum

Contents

Context

Vacua

Algebraic Qunantum 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

A vacuum state for an interacting field theory is sometimes called, for emphasis, an interacting vacuum.

In perturbative quantum field theory one starts with a free field theory and a vacuum state (or Hadamard vacuum state) on that, the “free vacuum”; and then finds, perturbatively, the interacting field algebra of observables. The free vacuum is typically still a state on the interacting field algebra of observables, but it is in general no longer a vacuum state with respect to the interacting field algebra. To highlight the difference to an actual vacuum state for the interacting field algebra, one speaks of the interacting vacuum (e.g. Rafelski 90).

Issues related to the adiabatic limit and infrared divergences in perturbative QFT are argued to be related to the need to pass to the correct interacting vacuum (Duch 17, p. 113-114).

This is understood to some extent in quantum electrodynamics but remains a major open problem in quantum chromodynamics (below).

Examples

In QCD

There are arguments that the phenomenon of confinement in QCD will be explained by finding the properly interacting vacuum of the perturbative theory (Rafelski 90, around pages 12-16). Possibly this is a “theta-vacuum” reflecting QCD instanton contributions (Schäfer-Shuryak 98, section III D).

References

Last revised on May 17, 2019 at 16:05:04. See the history of this page for a list of all contributions to it.