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Stochastic Analysis and Applications pp 45–50Cite as

Generalised Weyl Operators

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Part of the book series: Lecture Notes in Mathematics ((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. Cockroft, AM and Hudson, RL, Quantum mechanical Wiener processes, J. Multivariate Anal. 7, 107–24 (1978).

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  2. Guichardet, A, Symmetric Hilbert spaces and related topics, LNM 261, Springer, Berlin (1972).

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  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).

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  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).

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  5. Hudson, RL and Parthasarathy, KR, Quantum Itô's formula and stochastic evolutions, submitted to CMP.

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  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).

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  7. Reed, M and Simon, B, Methods of modern mathematical physics, Fourier analysis and self-adjointness, Academic Press, New York (1975).

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  8. Segal, IE, Tensor algebras over Hilbert space I, Trans. Amer. Math. Soc. 81, 106–34 (1956).

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Author information

Authors and Affiliations

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

    RL Hudson

  2. Indian Statistical Institute, 7, S.J.S. Sansanwal Marg, 110016, New Delhi, India

    KR Parthasarathy

Authors
  1. RL Hudson
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  2. KR Parthasarathy
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Editor information

Aubrey Truman David Williams

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© 1984 Springer-Verlag

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Hudson, R., Parthasarathy, K. (1984). Generalised Weyl Operators. In: Truman, A., Williams, D. (eds) Stochastic Analysis and Applications. Lecture Notes in Mathematics, vol 1095. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099121

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  • DOI: https://doi.org/10.1007/BFb0099121

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13891-4

  • Online ISBN: 978-3-540-39103-6

  • eBook Packages: Springer Book Archive

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