Geometry of Quantum Theory

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Geometry of Quantum Theory

Geometry of Quantum Theory

  • Author: V.S. Varadarajan
  • Publisher: Springer Science & Business Media
  • ISBN: 0387493867
  • Category: Science
  • Page: 412
  • View: 1076
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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

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Geometry of Quantum States

Geometry of Quantum States

An Introduction to Quantum Entanglement

  • Author: Ingemar Bengtsson,Karol Zyczkowski
  • Publisher: Cambridge University Press
  • ISBN: 1139453467
  • Category: Science
  • Page: N.A
  • View: 3121
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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.

Geometry of Quantum States

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Geometry of Quantum States

Geometry of Quantum States

An Introduction to Quantum Entanglement

  • Author: Ingemar Bengtsson,Karol Życzkowski
  • Publisher: Cambridge University Press
  • ISBN: 1108293492
  • Category: Science
  • Page: N.A
  • View: 1555
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Quantum information theory is a branch of science at the frontier of physics, mathematics, and information science, and offers a variety of solutions that are impossible using classical theory. This book provides a detailed introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. The second edition contains new sections and entirely new chapters: the hot topic of multipartite entanglement; in-depth discussion of the discrete structures in finite dimensional Hilbert space, including unitary operator bases, mutually unbiased bases, symmetric informationally complete generalized measurements, discrete Wigner function, and unitary designs; the Gleason and Kochen–Specker theorems; the proof of the Lieb conjecture; the measure concentration phenomenon; and the Hastings' non-additivity theorem. This richly-illustrated book will be useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied.

Quantum Mechanics in the Geometry of Space-Time

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Quantum Mechanics in the Geometry of Space-Time

Quantum Mechanics in the Geometry of Space-Time

Elementary Theory

  • Author: Roger Boudet
  • Publisher: Springer Science & Business Media
  • ISBN: 9783642191992
  • Category: Science
  • Page: 119
  • View: 3468
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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.

Quantum Physics and Geometry

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Quantum Physics and Geometry

Quantum Physics and Geometry

  • Author: Edoardo Ballico,Alessandra Bernardi,Iacopo Carusotto,Sonia Mazzucchi,Valter Moretti
  • Publisher: Springer
  • ISBN: 3030061221
  • Category: Science
  • Page: 173
  • View: 3954
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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.

Geometric and Algebraic Topological Methods in Quantum Mechanics

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Geometric and Algebraic Topological Methods in Quantum Mechanics

Geometric and Algebraic Topological Methods in Quantum Mechanics

  • Author: Giovanni Giachetta,Luigi Mangiarotti,Gennadi Sardanashvily
  • Publisher: World Scientific
  • ISBN: 9814481149
  • Category: Science
  • Page: 720
  • View: 1194
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' In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry's geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization. Contents:Commutative GeometryClassical Hamiltonian SystemsAlgebraic QuantizationGeometry of Algebraic QuantizationGeometric QuantizationSupergeometryDeformation QuantizationNon-Commutative GeometryGeometry of Quantum Groups Readership: Theoreticians and mathematicians of postgraduate and research level. Keywords:Algebraic Quantum Theory;Poisson Manifold;Hilbert Manifold;Geometric Quantization;Deformation Quantization;Supergeometry;Noncommutative Geometry;Constraint System;Quantum GroupKey Features:The book collects all the advanced methods of quantization in the last decadeIt presents in a compact way all the necessary up to date mathematical tools to be used in studying quantum problems.Reviews:“This book is well-written and I am convinced that it will be useful to all those interested in quantum theory.”Zentralblatt MATH “With respect to a propsective reader having a reasonably good background in mathematics, the notions, concepts, etc, are introduced in a self-contained but condensed manner … The book gives a very helpful supply of mathematical tools needed by a theoretical or mathematical physicist to effect entry into some of the new directions in theoretical physics. Also, a mathematician might appreciate the condensed presentation of definitions and results in one of the modern fields of mathematics for which one may be seeking an overview.”Mathematical Reviews '

Quantum Mechanics, Quantum Field Theory

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Quantum Mechanics, Quantum Field Theory

Quantum Mechanics, Quantum Field Theory

Geometry, Language, Logic

  • Author: R. Mirman
  • Publisher: iUniverse
  • ISBN: 0595336906
  • Category: Science
  • Page: 344
  • View: 4297
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The author does not want a book description on the back cover.

Geometry Of Quantum Potential, The: Entropic Information Of The Vacuum

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Geometry Of Quantum Potential, The: Entropic Information Of The Vacuum

Geometry Of Quantum Potential, The: Entropic Information Of The Vacuum

  • Author: Fiscaletti Davide
  • Publisher: World Scientific
  • ISBN: 9813227990
  • Category: Science
  • Page: 344
  • View: 7978
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In virtue of its features, Bohm's quantum potential introduces interesting and relevant perspectives towards a satisfactory geometrodynamic description of quantum processes. This book makes a comprehensive state-of-the-art review of some of the most significant elements and results about the geometrodynamic picture determined by the quantum potential in various contexts. Above all, the book explores the perspectives about the fundamental arena subtended by the quantum potential, the link between the geometry associated to the quantum potential and a fundamental quantum vacuum. After an analysis of the geometry subtended by the quantum potential in the different fields of quantum physics (the non-relativistic domain, the relativistic domain, the relativistic quantum field theory, the quantum gravity domain and the canonical quantum cosmology), in the second part of the book, a recent interpretation of Bohm's quantum potential in terms of a more fundamental entity called quantum entropy, the approach of the symmetryzed quantum potential and the link between quantum potential and quantum vacuum are analysed, also in the light of the results obtained by the author. Contents: Introduction The Geometry of the Quantum Potential in Different Contexts Quantum Entropy and Quantum Potential Immediate Quantum Information and Symmetryzed Quantum Potential The Quantum Potential ... and the Quantum Vacuum Conclusions References Index Readership: Researchers interested in the link between the geometrodynamic action of the quantum potential and a fundamental quantum vacuum, in the different contexts of quantum physics. Keywords: Entropy;Quantum;Potential;Symmetry;Geometry;GeometrodynamicReview: Key Features: This book provides a complete guide to the geometrodynamic features of the quantum potential as key of reading and understanding of the different fields of quantum physics To explore relevant perspectives about the fundamental arena of quantum processes which determines the action of the quantum potential and its geometry This book introduces, in the light of relevant current research, interesting and novel perspectives as regards the link between the geometrodynamic action of the quantum potential and a fundamental quantum vacuum, in the different contexts of quantum physics

Symplectic Geometry and Quantum Mechanics

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Symplectic Geometry and Quantum Mechanics

Symplectic Geometry and Quantum Mechanics

  • Author: Maurice A. de Gosson
  • Publisher: Springer Science & Business Media
  • ISBN: 3764375752
  • Category: Mathematics
  • Page: 368
  • View: 6484
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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.

Geometric Phases in Classical and Quantum Mechanics

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Geometric Phases in Classical and Quantum Mechanics

Geometric Phases in Classical and Quantum Mechanics

  • Author: Dariusz Chruscinski,Andrzej Jamiolkowski
  • Publisher: Springer Science & Business Media
  • ISBN: 0817681760
  • Category: Mathematics
  • Page: 337
  • View: 2705
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Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.