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Unification of fermion and Boson stochastic calculus

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Abstract

Fermion annihilation and creation processes are explicitly realised in Boson Fock space as functions of the corresponding Boson processes and second quantisations of reflections. Conversely, Boson annihilation and creation processes can be constructed from the Fermion processes. The existence of unitary stochastic evolutions driven by Fermion and gauge noise is thereby reduced to an equivalent Boson problem, which is then solved.

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Authors and Affiliations

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

    R. L. Hudson

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

    K. R. Parthasarathy

Authors
  1. R. L. Hudson
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  2. K. R. Parthasarathy
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Additional information

Communicated by H. Araki

This work was carried out while both authors were participating in the Symposium on Stochastic Differential Equations at the University of Warwick. The first author acknowledges conversations with R.F. Streater during the same Symposium

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Hudson, R.L., Parthasarathy, K.R. Unification of fermion and Boson stochastic calculus. Commun.Math. Phys. 104, 457–470 (1986). https://doi.org/10.1007/BF01210951

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  • DOI: https://doi.org/10.1007/BF01210951

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