nLab
KMS 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

Measure and probability theory

Vacua

Contents

Idea

A KMS state (named after Kubo 57, Martin-Schwinger 59) is a vacuum state for a relativistic quantum field theory describing thermal equilibrium at some positive temperature TT.

The final formulation of the KMS condition, now widely accepted, is due to Haag-Hugenholtz-Winnink 67.

Under Wick rotation (if applicable) a relativistic field theory on Minkowski spacetime d,1\mathbb{R}^{d,1} in a KMS state at temperature TT is identified with a Euclidean field theory on the product space d×S β 1\mathbb{R}^d \times S^1_{\beta} with a “compact/periodic Euclidean time” circle S β 1S^1_\beta of length β=1/T\beta = 1/T, this is essentially the KMS condition (see Fulling-Ruijsenaars 87). This relation is the basis of thermal quantum field theory, see there for more.

References

The formulation of the KMS condition is due to

  • R. Kubo Statistical-Mechanical Theory of Irreversible Processes I. General Theory and Simple Applications to Magnetic and Conduction Problems, Journal of the Physical Society of Japan 12, 570-586 1957

  • Paul C. Martin, Julian Schwinger, Theory of Many-Particle Systems. I, Physical Review 115, 1342-1373 (1959)

and found its final, now generally accepted, form in

  • Rudolf Haag, N. M. Hugenholtz, M. Winnink, On the equilibrium states in quantum statistical mechanics, Comm. Math. Phys. Volume 5, Number 3 (1967), 215-236 (euclid:1103840050)

A good quick survey, putting the KMS states into context with Wick rotation and thermal quantum field theory, is

  • S.A. Fulling, S.N.M. Ruijsenaars, Temperature, periodicity and horizons, Physics Reports Volume 152, Issue 3, August 1987, Pages 135-176 (pdf, doi:10.1016/0370-1573(87)90136-0)

See also

Last revised on May 17, 2019 at 16:08:53. See the history of this page for a list of all contributions to it.