Debashish Goswami's Books

Quantum Stochastic Processes and Noncommutative Geometry

By: Kalyan B. Sinha,Debashish Goswami

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Quantum Stochastic Processes and Noncommutative Geometry

By: Kalyan B. Sinha,Debashish Goswami

The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics.

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Page Count

301

Publisher

Cambridge University Press

Published Date

ISBN 10

1139461699

ISBN 13

9781139461696

Quantum Isometry Groups

By: Debashish Goswami,Jyotishman Bhowmick

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Quantum Isometry Groups

By: Debashish Goswami,Jyotishman Bhowmick

This book offers an up-to-date overview of the recently proposed theory of quantum isometry groups. Written by the founders, it is the first book to present the research on the “quantum isometry group”, highlighting the interaction of noncommutative geometry and quantum groups, which is a noncommutative generalization of the notion of group of isometry of a classical Riemannian manifold. The motivation for this generalization is the importance of isometry groups in both mathematics and physics. The framework consists of Alain Connes’ “noncommutative geometry” and the operator-algebraic theory of “quantum groups”. The authors prove the existence of quantum isometry group for noncommutative manifolds given by spectral triples under mild conditions and discuss a number of methods for computing them. One of the most striking and profound findings is the non-existence of non-classical quantum isometry groups for arbitrary classical connected compact manifolds and, by using this, the authors explicitly describe quantum isometry groups of most of the noncommutative manifolds studied in the literature. Some physical motivations and possible applications are also discussed.

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Page Count

254

Publisher

Springer

Published Date

ISBN 10

813223667X

ISBN 13

9788132236672

Quantum Stochastic Processes and Noncommutative Geometry

By: Kalyan B. Sinha,Debashish Goswami

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Quantum Stochastic Processes and Noncommutative Geometry

By: Kalyan B. Sinha,Debashish Goswami

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

301

Publisher

Cambridge University Press

Published Date

ISBN 10

1139461699

ISBN 13

9781139461696

Quantum Isometry Groups

By: Debashish Goswami,Jyotishman Bhowmick

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Quantum Isometry Groups

By: Debashish Goswami,Jyotishman Bhowmick

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

254

Publisher

Springer

Published Date

ISBN 10

813223667X

ISBN 13

9788132236672

Book's by Debashish Goswami

Quantum Stochastic Processes and Noncommutative Geometry

Quantum Stochastic Processes and Noncommutative Geometry

Quantum Isometry Groups

Quantum Isometry Groups

Quantum Stochastic Processes and Noncommutative Geometry

Quantum Stochastic Processes and Noncommutative Geometry

Quantum Isometry Groups

Quantum Isometry Groups

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