algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
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 $T$.
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 $\mathbb{R}^{d,1}$ in a KMS state at temperature $T$ is identified with a Euclidean field theory on the product space $\mathbb{R}^d \times S^1_{\beta}$ with a “compact/periodic Euclidean time” circle $S^1_\beta$ of length $\beta = 1/T$, this is essentially the KMS condition (see Fulling-Ruijsenaars 87). This relation is the basis of thermal quantum field theory, see there for more.
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
A good quick survey, putting the KMS states into context with Wick rotation and thermal quantum field theory, is
See also
Wikipedia KMS state, Tomita-Takesaki theory
Martin Bordemann, Hartmann Römer, Stefan Waldmann, KMS states and star product quantization, Reports on Mathematical Physics 44, n. 1-2 (1999) 45-52, doi
W. Pusz, S. L. Woronowicz, Passive states and KMS states for general quantum systems, Commun. Math. Phys. 58 (1978), no. 3, 273–290, MR471796, euclid
S. L. Woronowicz, On the existence of KMS states, Letters on Math. Phys. 10, no 1, 29–31 (1985) MR86m:46066, euclid, doi
Alain Connes, Matilde Marcolli, Noncommutative geometry, quantum fields and motives, Amer. Math. Soc. Coll. Publ. 55, 2008. xxii+785 pp. gBooks, draft pdf
Matthew Eric Bassett, math blog: KMS states and symmetries, Class Field Theory and the Bost-Connes System
Neverendingbooks blog KMS, Gibbs and zeta function
Last revised on November 9, 2018 at 11:10:44. See the history of this page for a list of all contributions to it.