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Lie algebras. --- Lie, Algèbres de --- Lie, Algèbres de. --- Lie, Algèbres de.

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Topological groups. Lie groups --- Lie groups. --- Lie, Groupes de. --- Representations of groups. --- Représentations de groupes. --- Lie groups --- Representations of groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups

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This book is an outgrowth of courses given by me for graduate students at York University in the past ten years. The actual writing of the book in this form was carried out at York University, Peking University, the Academia Sinica in Beijing, the University of California at Irvine, Osaka University, and the University of Delaware. The idea of writing this book was ?rst conceived in the summer of 1989, and the protracted period of gestation was due to my daily duties as a professor at York University. I would like to thank Professor K. C. Chang, of Peking University; Professor Shujie Li, of the Academia Sinica in Beijing; Professor Martin Schechter, of the University of California at Irvine; Professor Michihiro Nagase, of Osaka University; and Professor M. Z. Nashed, of the University of Delaware, for providing me with stimulating environments for the exchange of ideas and the actual writing of the book. We study in this book the properties of pseudo-differential operators arising in quantum mechanics, ?rst envisaged in [33] by Hermann Weyl, as bounded linear 2 n operators on L (R ). Thus, it is natural to call the operators treated in this book Weyl transforms.

Fourier analysis --- Pseudodifferential operators --- Fourier analysis. --- Pseudodifferential operators. --- Mathematics. --- Topological groups. --- Lie groups. --- Topological Groups, Lie Groups. --- Topological Groups. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Analysis, Fourier --- Mathematical analysis --- Operators, Pseudodifferential --- Pseudo-differential operators --- Operator theory

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This book describes the representations of Lie superalgebras that are yielded by a graded version of Hudson-Parthasarathy quantum stochastic calculus. Quantum stochastic calculus and grading theory are given concise introductions, extending readership to mathematicians and physicists with a basic knowledge of algebra and infinite-dimensional Hilbert spaces. The develpment of an explicit formula for the chaotic expansion of a polynomial of quantum stochastic integrals is particularly interesting. The book aims to provide a self-contained exposition of what is known about Z_2-graded quantum stochastic calculus and to provide a framework for future research into this new and fertile area.

Stochastic processes --- Quantum theory --- Mathematical physics --- Dynamique quantique --- Fysica [Mathematische ] --- Fysica [Wiskundige ] --- Mathematische fysica --- Mécanique des quanta --- Mécanique quantique --- Physical mathematics --- Physics -- Mathematics --- Physics [Mathematical ] --- Physique -- Mathématiques --- Physique -- Méthodes mathématiques --- Physique mathématique --- Physique théorique --- Processus stochastiques --- Quanta [Théorie des ] --- Quantum dynamics --- Quantum mechanics --- Quantumtheorie --- Stochastische processen --- Théorie des quanta --- Théorie quantique --- Wiskundige fysica --- Probabilities. --- Quantum computers. --- Spintronics. --- Quantum physics. --- Topological groups. --- Lie groups. --- Probability Theory and Stochastic Processes. --- Quantum Information Technology, Spintronics. --- Quantum Physics. --- Topological Groups, Lie Groups. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Fluxtronics --- Magnetoelectronics --- Spin electronics --- Spinelectronics --- Microelectronics --- Nanotechnology --- Computers --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Stochastic processes. --- Quantum theory. --- Mathematical physics. --- Random processes --- Probabilities