Geometry of Quantum Theory

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Author: V.S. Varadarajan

Publisher: Springer Science & Business Media

ISBN: 0387493867

Category: Science

Page: 412

View: 4929

Available for the first time in soft cover, this book is a classic on the foundations of quantum theory. It examines the subject from a point of view that goes back to Heisenberg and Dirac and whose definitive mathematical formulation is due to von Neumann. This view leads most naturally to the fundamental questions that are at the basis of all attempts to understand the world of atomic and subatomic particles.

Geometry of Quantum States

An Introduction to Quantum Entanglement

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Author: Ingemar Bengtsson,Karol Zyczkowski

Publisher: Cambridge University Press

ISBN: 1139453467

Category: Science

Page: N.A

View: 6700

Quantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory. This book provides an introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. After a gentle introduction to the necessary mathematics the authors describe the geometry of quantum state spaces. Focusing on finite dimensional Hilbert spaces, they discuss the statistical distance measures and entropies used in quantum theory. The final part of the book is devoted to quantum entanglement - a non-intuitive phenomenon discovered by Schrödinger, which has become a key resource for quantum computation. This richly-illustrated book is useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied.

From Geometry to Quantum Mechanics

In Honor of Hideki Omori

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Author: Yoshiaki Maeda,Peter Michor,Takushiro Ochiai,Akira Yoshioka

Publisher: Springer Science & Business Media

ISBN: 0817645306

Category: Mathematics

Page: 324

View: 647

* Invited articles in differential geometry and mathematical physics in honor of Hideki Omori * Focus on recent trends and future directions in symplectic and Poisson geometry, global analysis, Lie group theory, quantizations and noncommutative geometry, as well as applications of PDEs and variational methods to geometry * Will appeal to graduate students in mathematics and quantum mechanics; also a reference

Symplectic Geometry and Quantum Mechanics

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Author: Maurice A. de Gosson

Publisher: Springer Science & Business Media

ISBN: 3764375752

Category: Mathematics

Page: 368

View: 2776

This book offers a complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a very readable introduction to symplectic geometry. Many topics are also of genuine interest for pure mathematicians working in geometry and topology.

Geometry and Quantum Field Theory

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Author: Daniel S. Freed,Karen K. Uhlenbeck,American Mathematical Society,Institute for Advanced Study (Princeton, N.J.)

Publisher: American Mathematical Soc.

ISBN: 9780821886830

Category: Science

Page: 459

View: 2910

The first title in a new series, this book explores topics from classical and quantum mechanics and field theory. The material is presented at a level between that of a textbook and research papers making it ideal for graduate students. The book provides an entree into a field that promises to remain exciting and important for years to come.

Geometry and Quantum Physics

Proceedings of the 38. Internationale Universitätswochen für Kern- und Teilchenphysik, Schladming, Austria, January 9–16, 1999

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Author: H. Gausterer,H. Grosse,L. Pittner

Publisher: Springer

ISBN: 3540465529

Category: Science

Page: 408

View: 3885

In modern mathematical physics, classical together with quantum, geometrical and functional analytic methods are used simultaneously. Non-commutative geometry in particular is becoming a useful tool in quantum field theories. This book, aimed at advanced students and researchers, provides an introduction to these ideas. Researchers will benefit particularly from the extensive survey articles on models relating to quantum gravity, string theory, and non-commutative geometry, as well as Connes' approach to the standard model.

Geometry of PDEs and Mechanics

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Author: Agostino Prastaro

Publisher: World Scientific

ISBN: 9789810225209

Category: Science

Page: 750

View: 8669

This volume presents the theory of partial differential equations (PDEs) from a modern geometric point of view so that PDEs can be characterized by using either technique of differential geometry or algebraic geometry. This allows us to recognize the richness of the structure of PDEs. It presents, for the first time, a geometric theory of non-commutative (quantum) PDEs and gives a general application of this theory to quantum field theory and quantum supergravity.

Quantum Mechanics in the Geometry of Space-Time

Elementary Theory

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Author: Roger Boudet

Publisher: Springer Science & Business Media

ISBN: 9783642191992

Category: Science

Page: 119

View: 9524

This book continues the fundamental work of Arnold Sommerfeld and David Hestenes formulating theoretical physics in terms of Minkowski space-time geometry. We see how the standard matrix version of the Dirac equation can be reformulated in terms of a real space-time algebra, thus revealing a geometric meaning for the “number i” in quantum mechanics. Next, it is examined in some detail how electroweak theory can be integrated into the Dirac theory and this way interpreted in terms of space-time geometry. Finally, some implications for quantum electrodynamics are considered. The presentation of real quantum electromagnetism is expressed in an addendum. The book covers both the use of the complex and the real languages and allows the reader acquainted with the first language to make a step by step translation to the second one.

Geometric Formulation of Classical and Quantum Mechanics

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Author: G. Giachetta,L. G. Magiaradze,Gennadi? Aleksandrovich Sardanashvili

Publisher: World Scientific

ISBN: 9814313726

Category: Science

Page: 392

View: 934

The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.