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A new form and a ⋆-algebraic structure of quantum stochastic integrals in Fock space

  • V. P. Belavkin
Conferenze

Abstract

An algebraic definition of the basic quantum process for the noncommutative stochastic calculus is given in terms of the Fock representation of a Lie ⋆-algebra of matrices in a pseudo-Euclidean space. An operator definition of the quantum stochastic integral is given and its continuity is proved in a projective limit uniform operator topology. A new form of quantum stochastic equations, revealing the ⋆-algebraic structure of quantum Ito's formula, is given.

Keywords

Continuous Operator Projective Limit Weak Operator Topology Quantum Stochastic Calculus Polarization Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Hudson R. S. andParthasarathy K. R.,Quantum Ito's formula and stochastic evolution. Commun. Math. Phys.93 (1984) 301–323.MathSciNetCrossRefMATHGoogle Scholar
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    Lindsay M. andMaassen H.,An integral kernel approach to noise, in: Quantum Probability and Applications III, eds. L. Accardi and W. von Waldenfels, Springer, Berlin 1988, pp. 192–208.CrossRefGoogle Scholar
  3. [3]
    Belavkin V. P.,Quantum stochastic calculus and quantum stochastic filtering. Preprint Centro Matematico V. Volterra, Dipartimento di Matematica, Università di Roma II, 1989.Google Scholar

Copyright information

© Birkhäuser-Verlag 1988

Authors and Affiliations

  • V. P. Belavkin
    • 1
  1. 1.Physics Department of Milan UniversityMilanItaly

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