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Quantum Stochastic Calculus as a Unifying Force in Physics and Probability

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The Concept of Probability

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 24))

Abstract

A survey is made of the theory of quantum stochastic calculus in Fock space developed by the author and K. R. Parthasarathy, together with some of its applications. Comparison with the classical Ito stochastic calculus of Brownian motion is emphasised, as is the power of the quantum theory to unify aspects of the classical theory of stochastic processes, Boson and Fermion second quantisation and dilations of quantum dynamical semigroups.

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References

  1. O. Bratteli and D.W. Robinson Operator algebras and quantum statistical mechanics II, Springer, Berlin (1979)

    MATH  Google Scholar 

  2. V. Gorini, A. Kossakowski and E. C. G Sudarshan, J. Math. Phys. 17, 1298 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  3. A. Einstein Annalen der Physik 17, 549, (1905)

    Article  ADS  Google Scholar 

  4. R. L. Hudson, ’Quantum diffusions and cohomology of algebras’, in Proceedings of 1st World Congress of Bernoulli Society, Tashkent 1986.

    Google Scholar 

  5. R. L. Hudson and M. Evans, ’Multidimensional quantum diffusions’, to appear in Quantum Probability (Oberwolfach) Proceedings 1987, ed. L. Accardi, Springer LNM.

    Google Scholar 

  6. R. L. Hudson K.R. and Parthasarathy Commun. Math. Phys. 93, 301 (1984)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. R. L. Hudson and K.R. Parthasarathy Acta Applicandre Math. 2, 353 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  8. R. L. Hudson and K.R. Parthasarathy Commun. Math. Phys. 104, 457 (1986)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  9. M. Lax Phys. Rev. 145, 111 (1965).

    MathSciNet  Google Scholar 

  10. G. Lindbald Commun. Math. Phys. 48, 119 (1976)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. J.M. Lindsay and K.R. Parthasarathy, ’The passage from random walk to diffusion in quantum probability II’, preprint.

    Google Scholar 

  12. L.R. Senitzky Phys. Rev. 119, 670 (1960)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. M. Smoluchowsky Annalen der Physik 25, 205 (1908)

    Article  ADS  Google Scholar 

  14. B. Wiener, J. Mathematics and Physics 2, 131 (1923)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Mathematics Department, University of Nottingham, University Park, Nottingham, NG7 2RD, England

    R. L. Hudson

Authors
  1. R. L. Hudson
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Editor information

Editors and Affiliations

  1. University of Ioannina, Greece

    E. I. Bitsakis

  2. National Hellenic Research Foundation and National Technical University, Athens, Greece

    C. A. Nicolaides

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© 1989 Kluwer Academic Publishers

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Hudson, R.L. (1989). Quantum Stochastic Calculus as a Unifying Force in Physics and Probability. In: Bitsakis, E.I., Nicolaides, C.A. (eds) The Concept of Probability. Fundamental Theories of Physics, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1175-8_24

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  • DOI: https://doi.org/10.1007/978-94-009-1175-8_24

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7023-2

  • Online ISBN: 978-94-009-1175-8

  • eBook Packages: Springer Book Archive

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