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Geometry of Quantum Theory

Geometry of Quantum Theory PDF Author: Veeravalli Seshadri Varadarajan
Publisher: Springer
ISBN: 9781461577089
Category : Science
Languages : en
Pages : 193

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Book Description
The present work is the first volume of a substantially enlarged version of the mimeographed notes of a course of lectures first given by me in the Indian Statistical Institute, Calcutta, India, during 1964-65. When it was suggested that these lectures be developed into a book, I readily agreed and took the opportunity to extend the scope of the material covered. No background in physics is in principle necessary for understand ing the essential ideas in this work. However, a high degree of mathematical maturity is certainly indispensable. It is safe to say that I aim at an audience composed of professional mathematicians, advanced graduate students, and, hopefully, the rapidly increasing group of mathematical physicists who are attracted to fundamental mathematical questions. Over the years, the mathematics of quantum theory has become more abstract and, consequently, simpler. Hilbert spaces have been used from the very beginning and, after Weyl and Wigner, group representations have come in conclusively. Recent discoveries seem to indicate that the role of group representations is destined for further expansion, not to speak of the impact of the theory of several complex variables and function-space analysis. But all of this pertains to the world of interacting subatomic particles; the more modest view of the microscopic world presented in this book requires somewhat less. The reader with a knowledge of abstract integration, Hilbert space theory, and topological groups will find the going easy.

Geometry of Quantum Theory

Geometry of Quantum Theory PDF Author: Veeravalli Seshadri Varadarajan
Publisher: Springer
ISBN: 9781461577089
Category : Science
Languages : en
Pages : 193

View

Book Description
The present work is the first volume of a substantially enlarged version of the mimeographed notes of a course of lectures first given by me in the Indian Statistical Institute, Calcutta, India, during 1964-65. When it was suggested that these lectures be developed into a book, I readily agreed and took the opportunity to extend the scope of the material covered. No background in physics is in principle necessary for understand ing the essential ideas in this work. However, a high degree of mathematical maturity is certainly indispensable. It is safe to say that I aim at an audience composed of professional mathematicians, advanced graduate students, and, hopefully, the rapidly increasing group of mathematical physicists who are attracted to fundamental mathematical questions. Over the years, the mathematics of quantum theory has become more abstract and, consequently, simpler. Hilbert spaces have been used from the very beginning and, after Weyl and Wigner, group representations have come in conclusively. Recent discoveries seem to indicate that the role of group representations is destined for further expansion, not to speak of the impact of the theory of several complex variables and function-space analysis. But all of this pertains to the world of interacting subatomic particles; the more modest view of the microscopic world presented in this book requires somewhat less. The reader with a knowledge of abstract integration, Hilbert space theory, and topological groups will find the going easy.

Geometry of Quantum Theory

Geometry of Quantum Theory PDF Author: V.S. Varadarajan
Publisher: Springer Science & Business Media
ISBN: 0387493867
Category : Science
Languages : en
Pages : 412

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Book Description
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.

Quantum Physics and Geometry

Quantum Physics and Geometry PDF Author: Edoardo Ballico
Publisher: Springer
ISBN: 3030061221
Category : Science
Languages : en
Pages : 173

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Book Description
This book collects independent contributions on current developments in quantum information theory, a very interdisciplinary field at the intersection of physics, computer science and mathematics. Making intense use of the most advanced concepts from each discipline, the authors give in each contribution pedagogical introductions to the main concepts underlying their present research and present a personal perspective on some of the most exciting open problems. Keeping this diverse audience in mind, special efforts have been made to ensure that the basic concepts underlying quantum information are covered in an understandable way for mathematical readers, who can find there new open challenges for their research. At the same time, the volume can also be of use to physicists wishing to learn advanced mathematical tools, especially of differential and algebraic geometric nature.

Geometry and Quantum Field Theory

Geometry and Quantum Field Theory PDF Author: Daniel S. Freed
Publisher: American Mathematical Soc.
ISBN: 9780821886830
Category : Science
Languages : en
Pages : 476

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Book Description
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 of Quantum States

Geometry of Quantum States PDF Author: Ingemar Bengtsson
Publisher: Cambridge University Press
ISBN: 1107026253
Category : Mathematics
Languages : en
Pages : 637

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Book Description
This new edition describes the space of quantum states and the theory of quantum entanglement from a geometric perspective.

From Geometry to Quantum Mechanics

From Geometry to Quantum Mechanics PDF Author: Yoshiaki Maeda
Publisher: Springer Science & Business Media
ISBN: 0817645306
Category : Mathematics
Languages : en
Pages : 324

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Book Description
* 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

Quantum Mechanics, Quantum Field Theory

Quantum Mechanics, Quantum Field Theory PDF Author: R. Mirman
Publisher: iUniverse
ISBN: 0595336906
Category : Science
Languages : en
Pages : 341

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Book Description
The author does not want a book description on the back cover.

Geometry and Quantum Field Theory

Geometry and Quantum Field Theory PDF Author: Daniel S. Freed
Publisher: American Mathematical Soc.
ISBN: 0821804006
Category : Science
Languages : en
Pages : 472

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Book Description
Exploring topics from classical and quantum mechnanics and field theory, this book is based on lectures presented in the Graduate Summer School at the Regional Geometry Institute in Park City, Utah, in 1991. The chapter by Bryant treats Lie groups and symplectic geometry, examining not only the connection with mechanics but also the application to differential equations and the recent work of the Gromov school. Rabin's discussion of quantum mechanics and field theory is specifically aimed at mathematicians. Alvarez describes the application of supersymmetry to prove the Atiyah-Singer index theorem, touching on ideas that also underlie more complicated applications of supersymmetry. Quinn's account of the topological quantum field theory captures the formal aspects of the path integral and shows how these ideas can influence branches of mathematics which at first glance may not seem connected. Presenting material at a level between that of textbooks and research papers, much of the book would provide excellent material for graduate courses. The book provides an entree into a field that promises to remain exciting and important for years to come.

Symplectic Geometry and Quantum Mechanics

Symplectic Geometry and Quantum Mechanics PDF Author: Maurice A. de Gosson
Publisher: Springer Science & Business Media
ISBN: 3764375752
Category : Mathematics
Languages : en
Pages : 368

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Book Description
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.

M-Theory and Quantum Geometry

M-Theory and Quantum Geometry PDF Author: Lárus Thorlacius
Publisher: Springer Science & Business Media
ISBN: 9780792364740
Category : Mathematics
Languages : en
Pages : 482

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Book Description
The fundamental structure of matter and spacetime at the shortest length scales remains an exciting frontier of basic research in theoretical physics. A unifying theme in this area is the quantisation of geometrical objects. The majority of contributions to this volume cover recent advances in superstring theory, which is the leading candidate for a unified description of all known elementary particles and interactions. The geometrical concept of one-dimensional extended objects (strings) has always been at the core of superstring theory, but recently the focus has shifted to include higher-dimensional objects (D-branes), which play a key role in non-perturbative dynamics of the theory. Related developments are also described in M-theory, our understanding of quantum effects in black-hole physics, gauge theory of the strong interaction, and the dynamic triangulation construction of the quantum geometry of spacetime.