Skip to main content
SpringerLink
Log in

Some markov processes and markov fields in quantum theory, group theory, hydrodynamics and C*-algebras

  • Conference paper
  • First Online:
Stochastic Integrals

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 851))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References to Ch. I

  1. J. Deny, Méthodes hilbertiennes en théorie du potentiel, pp. 122–201 in Potential Theory, Ed. M. Brelot, Stresa 1969, C.I.M.E., Edizioni Cremonese, Roma 1970.

    Google Scholar 

  2. M. Fukushima, Dirichlet forms and Markov processes, North-Holland/Kodansha, Amsterdam / Tokyo (1980)

    MATH  Google Scholar 

  3. M.L. Silverstein, Symmetric Markov Processes, Lecture Notes in Maths. 426, Springer, Berlin (1974)

    MATH  Google Scholar 

  4. M.L. Silverstein, Boundary Theory for Symmetric Markov Processes, Lecture Notes in Maths. 516, Springer, Berlin (1976)

    MATH  Google Scholar 

  5. M. Fukushima, these Proceedings.

    Google Scholar 

  6. S. Albeverio, R. Høegh-Krohn, L. Streit, Energy forms, Hamiltonians and distorted Brownian paths, J. Math. Phys. 18, 907–917 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  7. K. Sato, see [I.2]

    Google Scholar 

  8. M.L. Silverstein, On the closability of Dirichlet forms, Z. Wahrscheinlichkeitsth. verw. Geb. 51, 185–200 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Fukushima, On distorted Brownian motions, to appear in Proc. Les Houches Workshop "Stochastic Equations in Physics", Phys. Repts.

    Google Scholar 

  10. M. Reed, B. Simon, Methods of Modern Mathematical Physics, Vol. IV: Analysis of Operators, Ch. XIII, 12, Academic Press, New York (1978); and references of Simon.

    MATH  Google Scholar 

  11. B. Simon, Brownian motions, Lp-properties of Schrödinger operators and the localization of binding, J. Funct. Anal. 35, 215–229 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  12. W. Heisenberg, W. Pauli, Zur Quantendynamik der Wellenfelder, Z. Phys. 56, 1–61 (1929)

    Article  MATH  Google Scholar 

  13. W. Heisenberg, W. Pauli, Zur Quantentehorie der Wellenfelder II, Z. Phys. 59, 168–190 (1930)

    Article  MATH  Google Scholar 

  14. K.O. Friedrichs, Mathematical aspects of the quantum theory of fields, Interscience, New York (1953)

    MATH  Google Scholar 

  15. I. Segal, Mathematical Problems of Relativistic Physics Am. Math. Soc., Providence (1963)

    MATH  Google Scholar 

  16. F. Coester, R. Haag, Representation of states in a field theory with canonical variables, Phys. Rev. 117, 1137–1145 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  17. H. Araki, Hamiltonian formalism and the canonical commutation relations in quantum field theory, J. Math. Phys. 1, 492–504 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  18. I.M. Gelfand, A.M. Yaglom, Integration in function spaces and its applications in quantum physics, J. Math. Phys. 1, 48–69 (1960)

    Article  MATH  Google Scholar 

  19. J. Glimm, A. Jaffe, Boson Quantum Field Models, pp. 77–143 in R.F. Streater ed., Mathematics of Contemporary Physics, Academic Press, New York (1972)

    Google Scholar 

  20. L. Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97, 1061–1083 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  21. W. Faris, Self-adjoint Operators, Lecture Notes in Maths. 433, Springer Berlin (1975) (and references therein)

    Google Scholar 

  22. J.P. Eckmann, Hypercontractivity for anharmonic osciallators, Helv. Phys. Acta 45, 1074–1088 (1974)

    Google Scholar 

  23. S. Albeverio, R. Høegh-Krohn, Quasi invariant measures, symmetric diffusion processes and quantum fields, pp. 11–59 in Proc. Intern. Coll. Math. Methods of Quantum Field Theory, CNRS (1976)

    Google Scholar 

  24. S. Albeverio, R. Høregh-Krohn, Dirichlet forms and diffusion processes on rigged Hilbert spaces, Z. f. Wahrscheinlichkeitstheorie verw. Geb. 40, 1–57 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  25. S. Albeverio, R. Høegh-Krohn, Hunt processes and analytic potential theory on rigged Hilbert spaces, Ann. Inst. H. Poincare B13, 269–291 (1977)

    MathSciNet  MATH  Google Scholar 

  26. P.A. Deift, Applications of a commutation formula, Duke math. J. 45, 267–310 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  27. S. Albeverio, R. Høegh-Krohn, L. Streit, Regularization of Hamiltonians and processes, J. Math. Phys. 21, 1636–1642 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  28. R. Carmona, Regularity properties of Schrödinger and Dirichlet semigroups, J. Funct. Anal. 33, 259–296 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  29. R. Carmona, Pointwise bounds for Schrödinger eigenstates, Comm. math., Phys. 62, 97–106 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  30. S. Albeverio, M. Fukushima, W. Karwowski, L. Streit, Capacity and quantum mechanical tunneling, Bochum Preprint (1980)

    Google Scholar 

  31. L. Streit, Energy forms: Schrödinger theory, processes, to appear in Proc. Les Houches Workshop "Stochastic Equations in Physics"; Phys. Repts.

    Google Scholar 

  32. S. Albeverio, R. Høegh-Krohn, Topics in infinite dimensional Analysis pp. 279–303 in Edts. G. Dell'Antonio, S. Doplicher, G. Jona-Lasinio, Mathematical Problems in Theoretical Physics, Lect. Notes Phys. 80, Springer, Berlin (1978).

    Chapter  Google Scholar 

  33. J.G. Hutton, Dirichlet forms associated with hypercontractive semigroups, Trans. Am. Math. Soc. 253, 237–256 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  34. G. Jona-Lasinio, F. Martinelli, E. Scoppola, New approach to the semi classical limit of quantum mechanics I Multiple tunneling in one dimension, Inst. Physics Rome Preprint (1980)

    Google Scholar 

  35. E. Nelson, Dynamical Theories of Brownian Motion, Princeton, (1967)

    Google Scholar 

  36. F. Guerra, P. Ruggiero, New interpretation of the Euclidean Markov field in the framework of physical Minkowski space-time Phys. Rev. Letts 31, 1022, (1973)

    Article  Google Scholar 

  37. S. Albeverio, R. Høegh-Krohn, A remark on the connection between stochastic mechanics and the heat equation, J. Math. Phys. 15, 1745–1747 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  38. F. Guerra, to appear in Proc. in Ref. [I.8]

    Google Scholar 

  39. Ph. Paclet, Espaces de Dirichlet et capacités fonctionnelles sur triplets de Hilbert-Schmidt, Sém. Krée (1978)

    Google Scholar 

  40. S. Kusuoka, Dirichlet forms and diffusion processes on Banach spaces, University of Tokyo Preprint (1980)

    Google Scholar 

  41. G.E. Uhlenbeck, L.S. Ornstein, On the theory of Brownian motion I, Phys. Rev. 36, 823–841 (1930)

    Article  MATH  Google Scholar 

  42. J.L. Doob, The Brownian movement and stochastic equations, Ann. of Math. 43, 351–369 (1942)

    Article  MathSciNet  MATH  Google Scholar 

  43. B. Simon, Functional integration and quantum physics, Academic Press, New York (1979)

    MATH  Google Scholar 

  44. P. Courrège, P. Renouard, Oscillateur anharmonique, mesures quasi-invariantes sur C(R,R) et théorie quantique des champs en dimension d=1, Astérisque 22–23, 1–245 (1976)

    MATH  Google Scholar 

  45. P. Priouret, M. Yor, Processus de diffusion à valeurs dans IR et mesures quasi-invariantes sur C(IR;IR), Astérisque 22–23, 247–290 (1976). For related work concerning quasi-invariant measures see also e.g.

    MATH  Google Scholar 

  46. G. Royer, Unicité de certaines mesures quasi-invariantes sur C(IR), Ann. Scient. Ec. Norm. Symp. 8, 319–338 (1975)

    MathSciNet  MATH  Google Scholar 

  47. M. Yor, Etudes de mesures de probabilité sur (ℝ *+ ;ℝ) quasi-invariantes sous les translations de (ℝ *+ ;ℝ), Ann. Inst. H. Poincaré B, 11, 127–172 (1975).

    Google Scholar 

  48. H.H. Kuo, Gaussian measures in Banach spaces, Lecture Notes in Mathematics 463, Springer, Berlin (1975).

    MATH  Google Scholar 

  49. E. Nelson, Probability theory and Euclidean field theory, pp. 94–124 in Edts. C. Velo, A. Wightman, Constructive quantum field theory, Proc. Erice School, Lecture Notes in Phys. 25, Springer, Berlin (1973)

    Chapter  Google Scholar 

  50. S. Albeverio, J.E. Fenstad, R. Høegh-Krohn, T. Lindstrøm, Nonstandard methods in stochastic analysis and mathematical physics, forthcoming book.

    Google Scholar 

  51. E. Nelson, The free Markov field, J. Funct. Anal. 12, 211–227 (1973) See also e.g.

    Article  MATH  Google Scholar 

  52. E. Wong, Homogeneous Gauss-Markov random fields, Ann. Math. Stat. 40, 1625–1634 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  53. E. Wong, Stochastic processes in information and dynamical systems, Ch. VII, McGraw Hill, New York (1971)

    MATH  Google Scholar 

  54. G.M. Molchan, Characterization of Gaussian fields with Markovian property, Dokl. Ak. Nauk SSR 197 (1971) (transl Sov. Math. Dokl. 12, 563–567 (1971)).

    Google Scholar 

  55. B. Simon, The P(ϕ)2 Euclidean (quantum) field theory, Princeton University Press (1974)

    Google Scholar 

  56. I.M. Gelfand, N.Ya. Vilenkin, Generalized functions, Vol. 4, Academic Press, New York (1964).

    Google Scholar 

  57. K. Symanzik, Euclidean quantum field theory, pp. 152–226 in Ed. R. Jost, Local Quantum Theory, Proc. Int. School E. Fermi, Academic Press, New York (1969)

    Google Scholar 

  58. F. Guerra, Unpublished. See also F. Guerra, Uniqueness of the vacuum energy density and van Hove phenomena in the infinite volume limit for two dimensional self-coupled Bose fields, Phys. Rev. Lett. 28, 1213 (1972)

    Article  Google Scholar 

  59. E. Nelson, Quantum fields and Markoff fields, pp. 413–420 in Ed. D. Spencer, Partial differential equations, Symp. Pure Math. 23, AMS Providence Rhode-Island (1973).

    Google Scholar 

  60. E. Nelson, Construction of quantum fields from Markoff fields, J. Funct. Anal. 12, 97–112 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  61. See e.g. J.P. Eckmann, H. Epstein, Time-ordered products and Schwinger functions, Comm. math. Phys. 64, 95–130 (1979); and references therein.

    Article  MathSciNet  Google Scholar 

  62. R. Høegh-Krohn, A general class of quantum fields without cut-offs in two space-time dimensions, Commun. math. Phys. 21, 244–251 (1971).

    Article  MathSciNet  Google Scholar 

  63. S. Albeverio, R. Høegh-Krohn, The Wightman axioms and the mass gap for strong interactions of exponential type in two dimensional space-time, J. Funct. Anal. 16, 39–82 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  64. S. Albeverio, R. Høegh-Krohn, Martingale convergence and the exponential interaction in IRn, pp. 331–353 in Ed. L. Streit, Quantum fields-Algebras, Processes, Springer, Wien (1980)

    Chapter  Google Scholar 

  65. S. Albeverio, G. Gallavotti, R. Høegh-Krohn, Some results for the exponential interaction in two or more dimensions, Commun. math. Phys. 70, 187–192 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  66. J. Fröhlich, C.M. Park, Remarks on the exponential interactions and the quantum Sine-Gordon equation in two space-time dimensions, Helv. Phys. Acta 50, 315–329 (1977).

    MathSciNet  Google Scholar 

  67. S. Albeverio, R. Høegh-Krohn, Uniqueness of the physical vacuum and the Wightman functions in the infinite volume limit for some non-polynomial interactions, Commun. math. Phys. 30, 171–Osipov 200 (1973)

    Google Scholar 

  68. J. Fröhlich, E. Seiler, The massive Thirring-Schwinger model (QED2): convergence of perturbation theory and particle structure, Helv. Phys. Acta 49, 889–924 (1976).

    MathSciNet  Google Scholar 

  69. E.P. Osipov, On the triviality of the:exp ϕ:4 quantum field theory in a finite volume, Novosibirsk Theor. Phys. Preprint (1979)

    Google Scholar 

  70. J. Glimm, A. Jaffe, T. Spencer, The particle structure of the weakly coupled ϕ2 model and other applications of high temperature expansions, im Buch Ref. I.22 a).

    Google Scholar 

  71. S. Albeverio, R. Høegh-Krohn, Uniqueness and the global Markov property for Euclidean fields. The case of trigonometric interactions, Commun. math. Phys. 68, 95–128 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  72. S. Albeverio, R. Høegh-Krohn, Canonical relativistic quantum fields, to appear in Ann. Inst. H. Poincaré A

    Google Scholar 

  73. S. Albeverio, R. Høegh-Krohn, Uniqueness of Gibbs states and global Markov property for Euclidean fields, to appear in Bolyai Math. Soc., Proc. Coll. "Random fields", Esztergom (1979)

    Google Scholar 

  74. S. Albeverio, R. Høegh-Krohn, Uniqueness and global Markov property for Euclidean fields and lattice systems, pp. 303–329 in Ref [I.26 c)]

    Google Scholar 

  75. J.P. Eckmann, Relativistic quantum fields in theories in two space-time dimensions, Quadermi CNR, Bologna (1977).

    Google Scholar 

  76. F. Guerra, L. Rosen, B. Simon, The P(ϕ)2 Euclidean quantum field theory as classical statistical mechanics, Ann. of Math. 101, 111–259 (1975).

    Article  MathSciNet  Google Scholar 

  77. J. Bellissard, R. Høegh-Krohn, in preparation.

    Google Scholar 

  78. R. Gielerak, in preparation

    Google Scholar 

  79. G. Wentzel, Quantum theory of fields, Interscience, New York (1949).

    MATH  Google Scholar 

  80. C. Newman, The construction of stationary two-dimensional Markoff fields with an application to quantum field theory, J. Funct. Anal. 14, 44–61 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  81. N. Dang Ngoc, G. Royer, Markov property of extremal local fields, Proc. Am. Math. Soc. 70, 185–188 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  82. G.C. Hegerfeld, From Euclidean to relativistic fields and the motion of Markoff fields, Comm. Math. Phys. 35, 155–171 (1974)

    Article  MathSciNet  Google Scholar 

  83. J. Fröhlich, Schwinger functions and their generating functionals, I. Helv. Phys. Acta 74, 265–306 (1976); Adv. Math. 23, 119–180 (1977)

    MathSciNet  MATH  Google Scholar 

  84. I. Segal, Non linear functions of weak processes I, J. Funct. Anal. 4, 404–451 (1969).

    Article  MATH  Google Scholar 

  85. R.L. Dobrushin, R.A. Minlos, Polynomials in linear random functions, Russ. Math. Surv. 32, 71–127 (1971).

    Article  MATH  Google Scholar 

  86. R.L. Dobrushin, R.A. Minlos, The moments and polynomials of generalized random field, Theory of Prob. & its Appl. 23, 686–699 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  87. S. Albeverio, R. Høegh-Krohn, G. Olsen, The global Markov property for lattice systems, J. Multiv. Anal.

    Google Scholar 

  88. J. Bellissard, P. Pico Lattice quantum fields: Uniqueness and Markov property, CNRS-CPT Marseille Preprint (Dec. 1978)

    Google Scholar 

  89. H. Föllmer, On the global Markov property pp.293–302 in Ref. [I.26 c)]

    Google Scholar 

  90. G.O.S. Ekhaguere, A characterization of Markovian homogeneous multicomponent Gaussian fields, Commun. math. Phys.73, 63–77, (1980)

    Article  MathSciNet  MATH  Google Scholar 

  91. D. Surgailis, On covariant stochastic differential equations and Markov property of their solutions, Vilnius-Rome Preprint (1979).

    Google Scholar 

  92. D. Williams, Diffusions, Markov processes and martingales, Vol. 1, J. Wiley, New York (1980)

    Google Scholar 

  93. K. Osterwalder, R. Schrader, Axioms for Euclidean Green's function II, CMP 42, 281–305 (1975)

    MathSciNet  MATH  Google Scholar 

  94. A. Klein, The semigroup characterization of Osterwalder-Schrader path spaces and the construction of Euclidean fields, J. Funct. Anal. 27, 277–291 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  95. H.v. Weizsäcker, A simple example concerning the global Markov property of lattice random fields, Kaiserslautern Preprint, to appear in Proc. Eigth Winter School in Abstract Analysis (1980).

    Google Scholar 

  96. R. Dobrushin, Prescribing a system of random variables by conditional distribution, Th. Prob. Appl. 15, 3, 485–486 (1970) (and references therein).

    Article  MathSciNet  MATH  Google Scholar 

  97. H.W. Goelden, On non-degeneracy of the ground state of Schrödinger operators, Math. Z. 155, 239–247 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  98. F. Gesztesy, On non-degenerate ground states for Schrödinger operators, to appear in Rep. Math. Phys.

    Google Scholar 

  99. S. Albeverio, R. Høegh-Krohn, Local and global Markoff fields, to appear in Rep. Math. Phys.

    Google Scholar 

  100. R.F. Streater, Euclidean quantum mechanics and stochastic integrals, these Proceedings.

    Google Scholar 

  101. T. Lindstrøm, A Loeb measure approach to theorems by Prokorov Sazonov and Gross, Oslo Univ. Prepr. (1980), to appear in Trans. Am. Math. Soc.

    Google Scholar 

  102. R. Ismagilov, On unitary representations of the group C ∞o , Math. Sb. 100 (2), 117–131 (1976) (transl. Math. USSR Sb 29, 105–117 (1976)).

    MathSciNet  MATH  Google Scholar 

  103. A. Vershik, I. Gelfand, M. Graev, Remarks on the representation of the groups of functions with values in a compact Lie group, to appear in Compos. Math.

    Google Scholar 

  104. S. Albeverio, R. Høegh-Krohn, The energy representation of Sobolev-Lie groups, Compositio Math. 36, 37–52 (1978)

    MathSciNet  MATH  Google Scholar 

  105. S. Albeverio, R. Høegh-Krohn, D. Testard, Irreducibility and reducibility for the energy representation of the group of mappings of a Riemannian manifold into a compact semisimple Lie group, Bochum Preprint (1979) (to appear in J. Funct. Anal.)

    Google Scholar 

  106. I.B. Frenkel, Orbital theory for affine Lie algebras, Yale Preprint (1980).

    Google Scholar 

  107. A. Guichardet, Symmetric Hilbert spaces and related topics, Lecture Notes in Maths. 261, Springer, Berlin (1972).

    MATH  Google Scholar 

  108. S. Albeverio, R. Høegh-Krohn, preprint 77/962 Marseille (November 1977).

    Google Scholar 

  109. E.B. Dynkin, Markov processes and random fields, Cornell Univ. Preprint (1979)

    Google Scholar 

  110. E.B. Dynkin, to appear in same issue of Phys. Repts. as [I.11 1)].

    Google Scholar 

  111. W.D. Wick, On the absolute continuity of a convolution with an infinite dimensional measure, Univ. of Washington, Seattle, Preprint (1979).

    Google Scholar 

  112. H.P. McKean, Jr.; Stochastic integrals, Academic Press, New York (1969).

    MATH  Google Scholar 

  113. S. Albeverio, A. Vershik, R. Høegh-Krohn, D. Testard, in preparation.

    Google Scholar 

  114. R.F. Streater, Current commutation relations, continuous tensor products, and infinitely divisible group representations, pp. 247–263 in R. Jost, Edt., Local Quantum Theory, Academic Press, New York (1969)

    Google Scholar 

  115. H. Araki, Factorisable representations of current algebra, Publ. RIMS, Kyoto, Ser. A, 5, 361–422 (1970).

    Article  MathSciNet  MATH  Google Scholar 

  116. K.R. Parthasarathy, K. Schmidt, Positive definite kernels, continuous tensor products, and central limit theorems of probability theory, Lect. Notes in Maths. 272, Springer, Berlin (1972).

    MATH  Google Scholar 

  117. S. Albeverio, M. De Faria, R. Eøegh-Krohn, Stationary measures for the periodic Euler flow in two dimensions, J. Stat. Phys. 20, 585–595 (1979).

    Article  MathSciNet  Google Scholar 

  118. S. Albeverio, R. Høegh-Krohn, Stochastic flows with stationary distribution, Bochum Preprint (1979)

    Google Scholar 

  119. T.D. Lee, On some statistical properties of hydrodynamical and magneto hydrodynamical fields, Quart. J. Appl. Math. 10, 69–74 (1952)

    MathSciNet  MATH  Google Scholar 

  120. R.H. Kraichnan, Remarks on turbulence theory, Adv. Math. 16, 305–331 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  121. H.M. Glaz, Two attempts at modeling two-dimensional turbulence, pp. 135–155 in Turbulence Seminar, Berkeley 1976/77, Lect. Notes in Maths. 615, Springer, Berlin (1977).

    Chapter  Google Scholar 

  122. G. Gallavotti, Problèmes ergodiques de la mècanique classique, Ens. 3ecycle Phys. Suisse Romande, Ec. Polyt. Féd., Lausanne (1976).

    Google Scholar 

  123. H.A. Rose, P.L. Sulem, Fully developed turbulence and statistical mechanics, J. de Phys. (Paris) 39, 441–484 (1978).

    Article  MathSciNet  Google Scholar 

  124. R.H. Kraichnan, D. Montgomery, Two-dimensional turbulence, Rep. Progr. Phys. 43, 547–619 (1979)

    Article  MathSciNet  Google Scholar 

  125. C. Boldrighini, Introduzione alla fluidodinamica Quaderni CNR, Roma (1979)

    MATH  Google Scholar 

  126. See also for recent work [III.4], [III.5]

    Google Scholar 

  127. C. Boldrighini, S. Frigio, Equilibrium states for the two dimensional in compressible Euler fluid, Atti Sem. Mat. Fis. Univ. Modena 27, 106–125 (1978)

    MathSciNet  MATH  Google Scholar 

  128. C. Boldrighini, S. Frigio, Equilibrium states for a plane incompressible perfect fluid, Commun. math. Phys. 72, 55–76 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  129. S. Albeverio, R. Høegh-Krohn, Let us talk about the weather — A model for large scale atmospheric features, to appear in Proc. Les Embiez Conference Disordered Systems (1980); and paper in preparation.

    Google Scholar 

  130. E. Hopf, Statistical hydrodynamics and functional calculus, J. Rat. Mech. Anal. 1, 87–123 (1952).

    MathSciNet  MATH  Google Scholar 

  131. C. Marchioro, A. Pellegrinotti, M. Pulvirenti, Self-adjointness of the Liouville operator for infinite classical systems, Commun. math. Phys. 58, 113–129 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  132. S. Albeverio, M. De Faria, R. Høegh-Krohn, in preparation.

    Google Scholar 

  133. S. Albeverio, R. Høegh-Krohn, Dirichlet forms and Markov semigroups on C*-algebras, Commun. math. Phys. 56, 173–187 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  134. G.G. Emch, Generalized K-flows, Commun. math. Phys. 49, 191–215 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  135. G.G. Emch, S. Albeverio, J.P. Eckmann, Quasi-free generalized K-flows, Rept. Math. Phys. 13, 73–85 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  136. E.B. Davies, Quantum theory of open systems, Academic Press, London (1976)

    MATH  Google Scholar 

  137. W. Arveson, Subalgebras of C*-algebras I, Acta Math. 123, 141–224 (1969); II, Acta Math. 12f, 271–30f (1972).

    Article  MathSciNet  MATH  Google Scholar 

  138. S. Albeverio, R. Høegh-Krohn, Frobenius theory for positive maps of von Neumann algebras, Commun. math. Phys. 64, 83–94 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  139. M. Enomoto, Y. Watatani, A Perron-Frobenius type theorem for positive linear maps on C*-algebras, Osaka Univ. Preprint (1978)

    Google Scholar 

  140. S. Albeverio, R. Høegh-Krohn, G. Olsen, Dynamical semigroups and Markov processes on C*-algebras, J. Reine und angew. Math. (Crelle's J.) 319, 25–37 (1980).

    MathSciNet  MATH  Google Scholar 

Download references

Authors
  1. Sergio Albeverio
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Raphael Høegh-Krohn
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

David Williams

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Albeverio, S., Høegh-Krohn, R. (1981). Some markov processes and markov fields in quantum theory, group theory, hydrodynamics and C*-algebras. In: Williams, D. (eds) Stochastic Integrals. Lecture Notes in Mathematics, vol 851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088741

Download citation

  • DOI: https://doi.org/10.1007/BFb0088741

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10690-6

  • Online ISBN: 978-3-540-38613-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation