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

  • V. P. Belavkin


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.


Continuous Operator Projective Limit Weak Operator Topology Quantum Stochastic Calculus Polarization Formula 
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    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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