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Quantum Stochastic Processes
Luigi Accardi (University of Rome Tor Vergata, Dublin Institute For Advanced Studies), Alberto Frigerio (University of Rome Tor Vergata, University of Milan), John T. Lewis (Dublin Institute For Advanced Studies, University of Milan)
Abstract: A class of non-commutative stochastic processes is defined.These processes are defined up to equivalence by their multi-time correlation kernels.A reconstruction theorem, generalizing the Kolmogorov theorem for classical processes, is proved.Markov processes and their associated semigroups are studied, and some non-quasi free examples are constructed on the Clifford algebra, with the use of a perturbation theory of Markov processes.The connection with the Hepp-Lieb models is discussed.