Author | Parthasarathy, K. R. author |
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Title | An Introduction to Quantum Stochastic Calculus [electronic resource] / by K. R. Parthasarathy |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1992 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8641-3 |
Descript | XI, 292 p. online resource |
I Events, Observables and States -- 1 From classical to quantum probability -- 2 Notational preliminaries -- 3 Finite dimensional quantum probability spaces -- 4 Observables in a simple quantum probability space -- 5 Variance and covariance -- 6 Dynamics in finite dimensional quantum probability spaces -- 7 Observables with infinite number of values and the Hahn-Hellinger Theorem -- 8 Probability distributions on? (?)and Gleasonโs Theorem -- 9 Trace class operators and Schattenโs Theorem -- 10 Spectral integration and Stoneโs Theorem on the unitary representations of ?pk -- 11 Basic notions of the theory of unbounded operators -- 12 Spectral integration of unbounded functions and von Neumannโs Spectral Theorem -- 13 Stone generators, characteristic functions and moments -- 14 Wignerโs Theorem on the automorphisms of ?(?) -- II Observables and States in Tensor Products of Hubert Spaces -- 15 Positive definite kernels and tensor products of Hilbert Spaces -- 16 Operators in tensor products of Hilbert Spaces -- 17 Symmetric and antisymmetric tensor products -- 18 Examples of discrete time quantum stochastic flows -- 19 The Fock Spaces -- 20 The Weyl Representation -- 21 Weyl Representation and infinitely divisible distributions -- 22 The symplectic group of ? and Shaleโs Theorem -- 23 Creation, conservation and annihilation operators in ?a(?) -- III Stochastic Integration and Quantum Itoโs Formula -- 24 Adapted processes -- 25 Stochastic integration with respect to creation, conservation and annihilation processes -- 26 A class of quantum stochastic differential equations -- 27 Stochastic differential equations with infinite degrees of freedom -- 28 Evans-Hudson Flows -- 29 A digression on completely positive linear maps and Stinespringโs Theorem -- 30 Generators of quantum dynamical semigroups and the Gorini, Kossakowski, Sudarshan, Lindblad Theorem -- References -- Author Index