nLab
vacuum state

Context

Algbraic 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

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

In quantum field theory a vacuum state is supposed to be a quantum state that expresses the absence of any particle excitations of the fields.

On Minkowski spacetime the vacuum state for a free field theory is the standard Hadamard state. On general globally hyperbolic spacetimes there are always Hadamard states, and they do play the role of the vacuum state in the construction of AQFT on curved spacetimes, see at locally covariant perturbative AQFT. Notably the choice of such a Hadamard state fixes the Feynman propagator, hence the time-ordered product of quantum observables and thus the perturbative S-matrix away from coinciding interaction points (the extension of these distributions to coinciding interaction points is the process of renormalization).

However, since on a general globally hyperbolic spacetime there is no globally well-defined concept of particles, there is in general no concept of vacuum state. But under good conditions (such as existence of suitable timelike Killing vectors) one may identify Hadamard states which deserve to be thought of as vacuum states (Brum-Fredenhagen 13).

References

Last revised on January 12, 2018 at 19:26:34. See the history of this page for a list of all contributions to it.