A new form and a ⋆-algebraic structure of quantum stochastic integrals in Fock space
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.
KeywordsContinuous Operator Projective Limit Weak Operator Topology Quantum Stochastic Calculus Polarization Formula
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