Abstract
Spectra of the generators of time translations (“Liouville operators”) on representation spaces determined by thermodynamic equilibrium states are compared and their nature is investigated.
Similar content being viewed by others
References
Powers, R.T., Sakai, S.: Existence of ground states and K.M.S.-states for approximately inner dynamics. Commun. math. Phys.39, 273–288 (1975)
Doplicher, S., Kastler, D., Robinson, D.W.: Covariance algebras in field theory and statistical mechanics. Commun. math. Phys.3, 1–28 (1966)
Kastler, D.: Equilibrium states of matter and operator algebras. Proceedings of the meeting onC*-algebras and their applications to theoretical physics. Rome, March 1975
Størmer, E.: Spectra of ergodic transformations. J. Funct. Anal.15, 202–215 (1974)
Araki, H., Woods, E.J.: Representations of the canonical commutation relations describing a non relativistic infinite free Bose gas. J. Math. Phys.4, 637 (1963)
Arveson, W.: On groups of automorphism of operator algebras. J. Funct. Anal.15, 217–243 (1974)
Takesaki, M., Winnink, M.: Local normality in quantum statistical mechanics. Commun. math. Phys.30, 129–152 (1973)
Haag, R., Hugenholtz, N.M., Winnink, M.: On the equilibrium states in quantum statistical mechanics. Commun. math. Phys.5, 215 (1967)
Takeda, Z.: Inductive limit and infinite direct product of operator algebras. Tôhoku Math. J.7, 67–86 (1955)
Kallman, R.R.: Uniform continuity, unitary groups, and compact operators. J. Funct. Anal.1, 245–253 (1967)
Bratteli, O., Robinson, D.W.: Unbounded derivations of von Neumann algebras. Preprint Marseille, June 1975
Robinson, D.W.: The approximation of flows. Preprint Marseille, November 1975
Hille, E., Phillips, R.S.: Functional analysis and semi-groups. Amer. Math. Soc. Colloq. Publ. Vol. XXXI (1957)
Haag, R., Kadison, R.V., Kastler, D.: Commun. math. Phys.16, 81 (1970)
Herman, R.H., Takesaki, M.: States and automorphism groups of operator algebras. Commun. math. Phys.19, 142–160 (1970)
Dixmier, J.: Les algèbres d'opérateurs dans l'espace hilbertien. Paris: Gauthier-Villars 1969
Sakai, S.:C*-algebras andW*-algebras. Berlin-Heidelberg-New York: Springer 1971
Halmos, P.R.: Measure theory. Princeton: van Nostrand 1950
Winnink, M.: Algebraic consequences of the K.M.S. boundary condition. In: Cargèse lectures in Physics, Vol. 4. Ed. D. Kastler. New York: Gordon and Breach 1970
Størmer, E.: Large groups of automorphisms ofC*-algebras. Commun. math. Phys.5, 1–22 (1967)
Winnink, M.: Almost equilibrium in an algebraic approach. In: Fundamental problems in statistical mechanics, Vol. 3. (ed. E.G.D. Cohen). Amsterdam: North-Holland Publishing Company 1975
Author information
Authors and Affiliations
Additional information
Communicated by J. L. Lebowitz
Rights and permissions
About this article
Cite this article
Brinke, G.t., Winnink, M. Spectra of Liouville operators. Commun.Math. Phys. 51, 135–150 (1976). https://doi.org/10.1007/BF01609344
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01609344