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Generalised Weyl Operators

  • RL Hudson
  • KR Parthasarathy
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1095)

Abstract

Using the quantum Itô's formula of [5] we construct operators satisfying a generalisation of the Weyl commutation relations, in which scalar-valued test functions are replaced by operator-valued ones.

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References

  1. [1]
    Cockroft, AM and Hudson, RL, Quantum mechanical Wiener processes, J. Multivariate Anal. 7, 107–24 (1978).MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Guichardet, A, Symmetric Hilbert spaces and related topics, LNM 261, Springer, Berlin (1972).CrossRefzbMATHGoogle Scholar
  3. [3]
    Hudson, RL, Karandikar, RL and Parthasarathy, KR, Towards a theory of noncommutative semimartingales adapted to Brownian motion and a quantum Itô's formula, in Theory and application of random fields, ed. Kallianpur, LN in Control and Information Sciences 49, Springer, Berlin (1983).Google Scholar
  4. [4]
    Hudson, RL and Parthasarathy, KR, Quantum diffusions, in Theory and application of rándom fields, ed. Kallianpur, LN in Control and Information Sciences 49 Springer, Berlin (1983).Google Scholar
  5. [5]
    Hudson, RL and Parthasarathy, KR, Quantum Itô's formula and stochastic evolutions, submitted to CMP.Google Scholar
  6. [6]
    Hudson, RL and Streater, RF, Noncommutative martingales and stochastic integrals in Fock space, in Stochastic processes in quantum theory and statistical physics, ed. Albeverio et al., LN in Physics 173, Springer, Berlin (1982).CrossRefGoogle Scholar
  7. [7]
    Reed, M and Simon, B, Methods of modern mathematical physics, Fourier analysis and self-adjointness, Academic Press, New York (1975).zbMATHGoogle Scholar
  8. [8]
    Segal, IE, Tensor algebras over Hilbert space I, Trans. Amer. Math. Soc. 81, 106–34 (1956).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • RL Hudson
    • 1
  • KR Parthasarathy
    • 2
  1. 1.Mathematics DepartmentUniversity of NottinghamNottingham
  2. 2.Indian Statistical InstituteNew DelhiIndia

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