Infinite Dimensional Groups and Algebras in Quantum Physics
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Superanalysis
This work can be recommended as an extensive course in superanalysis, the theory of functions of commuting and anticommuting variables. It follows the so-called functional superanalysis which was developed by J. Schwinger, B. De Witt, A. Rogers, V.S. Vladimirov and I.V. Volovich, Yu. Kobayashi and S. Nagamashi, M. Batchelor, U. Buzzo and R. Cianci and the present author. In this approach, superspace is defined as a set of points on which commuting and anticommuting coordinates are given. Thus functional superanalysis is a natural generalization of Newton's analysis (on real space) and strongly differs from the so-called algebraic analysis which has no functions of superpoints, and where 'functions' are just elements of Grassmann algebras. This volume is important for quantum physics in that it offers the possibility of extending the notion of space, and of operating on spaces which are described by noncommuting coordinates. These supercoordinates, which are described by an infinite number of ordinary real, complex or p-adic coordinates, are interpreted as creation or annihilation operators of quantum field theory. Subjects treated include differential calculus, including Cauchy-Riemann conditions, on superspaces over supercommutative Banach and topological superalgebras; integral calculus, including integration of differential forms; theory of distributions and linear partial differential equations with constant coefficients; calculus of pseudo-differential operators; analysis on infinite-dimensional superspaces over supercommutative Banach and topological supermodules; infinite-dimensional superdistributions and Feynman integrals with applications to superfield theory; noncommutative probabilities (central limit theorem); and non-Archimedean superanalysis. Audience: This volume will be of interest to researchers and postgraduate students whose work involves functional analysis, Feynman integration and distribution theory on infinite-dimensional (super)spaces and its applications to quantum physics, supersymmetry, superfield theory and supergravity.
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Group Theory and Hopf Algebra: Lectures for Physicists
A unique aspect of the book is its treatment of Hopf algebras in a form accessible to physicists. Hopf algebras are generalizations of groups and their concepts are acquiring importance in the treatment of conformal field theories, noncommutative spacetimes, topological quantum computation and other important domains of investigation. But there is a scarcity of treatments of Hopf algebras at a level and in a manner that physicists are comfortable with. This book addresses this need superbly. There are illustrative examples from physics scattered throughout the book and in its set of problems. It also has a good bibliography. These features should enhance its value to readers. The authors are senior physicists with considerable research and teaching experience in diverse aspects of fundamental physics. The book, being the outcome of their combined efforts, stands testament to their knowledge and pedagogical skills.
Quantum Independent Increment Processes II: Structure of Quantum Levy Processes, Classical Probability, and Physics
This is the second of two volumes containing the revised and completed notes of lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald in March, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics....
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Lie Groups, Lie Algebras, and Their Representation
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Chihiro Hamaguchi, "Basic Semiconductor Physics, 2nd edition"
Optical and transport properties, magneto-transport, two dimensional electron gas transport (HEMT and MOSFET), and quantum transport are reviewed, explaining optical transition, electron phonon interactions, electron mobility. Recent progress in quantum structures such as two-dimensional electron gas, superlattices, quantum Hall effect, electron confinement and the Landauer formula are included. The Quantum Hall effect is presented with different models. In the second edition, the addition energy and electronic structure of a quantum dot (artificial atom) are explained with the help of Slater determinants. Also the physics of semiconductor Lasers is described in detail including Einstein coefficients, stimulated emission, spontaneous emission, laser gain, double heterostructures, blue Lasers, optical confinement, laser modes, strained quantum wells lasers which will give insight into the physics of various kinds of semiconductor lasers, in addition to the various processes of luminescence.
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Finite or Infinite Dimensional Complex Analysis
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Hermann Weyl, "The Classical Groups: Their Invariants and Representations
In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics.
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Quantum Probability And Infinite Dimensional Analysis: From Foundations To Applications
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Operator Algebras and Quantum Statistical Mechanics 2: Equilibrium States by Ola Bratteli
For almost two decades this has been the classic textbook on applications of operator algebra theory to quantum statistical physics. It describes the general structure of equilibrium states, the KMS condition and stability, quantum spin systems and continuous systems. Major changes in the new edition relate to the Bose-Einstein condensation, the dynamics of the X-Y model and questions about phase transitions. The Notes and Remarks have been considerably augmented.
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Modern Quantum Mechanics, 2nd Edition
Jim Napolitano earned an undergraduate Physics degree at Rensselaer Polytechnic Institute in 1977, and a PhD in Physics from Stanford University in 1982. Since that time, he has conducted research in experimental nuclear and particle physics, with an emphasis on studying fundamental interactions and symmetries. He joined the faculty at Rensselaer in 1992 after working as a member of the scientific staff at two different national laboratories. He is author and co-author of over 150 scientific papers in refereed journals. Professor Napolitano maintains a keen interest in science education in general, and in particular physics education at both the undergraduate and graduate levels. He has published a textbook, co-authored with Adrian Melissinos, on Experiments in Modern Physics. Prior to his work on Modern Quantum Mechanics,Second Edition, he has taught both graduate and upper-level undergraduate courses in Quantum Mechanics, as well as an advanced graduate course in Quantum Field Theory.
Quantum Computation and Quantum Information: 10th Anniversary Edition
Quantum mechanics and computer science are introduced before moving on to describe what a quantum computer is, how it can be used to solve problems faster than 'classical' computers and its real-world implementation. It concludes with an in-depth treatment of quantum information. Containing a wealth of figures and exercises, this well-known textbook is ideal for courses on the subject, and will interest beginning graduate students and researchers in physics, computer science, mathematics, and electrical engineering.
Quantum Gravity in 2+1 Dimensions
This timely volume provides a broad survey of (2+1)-dimensional quantum gravity. It emphasises the 'quantum cosmology' of closed universes and the quantum mechanics of the (2+1)-dimensional black hole. It compares and contrasts a variety of approaches, and examines what they imply for a realistic theory of quantum gravity. General relativity in three spacetime dimensions has become a popular arena in which to explore the ramifications of quantum gravity. As a diffeomorphism-invariant theory of spacetime structure, this model shares many of the conceptual problems of realistic quantum gravity. But it is also simple enough that many programs of quantization can be carried out explicitly. After analysing the space of classical solutions, this book introduces some fifteen approaches to quantum gravity - from canonical quantization in York's 'extrinsic time' to Chern-Simons quantization, from the loop representation to covariant path integration to lattice methods. Relationships among quantizations are explored, as well as implications for such issues as topology change and the 'problem of time'. This book is an invaluable resource for all graduate students and researchers working in quantum gravity.
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Electronic Properties of Engineering Materials
The second part introduces Quantum mechanics and applies Quantum chemistry and Quantum physics to the basic properties of metals, insulators, and semiconductors. This approach allows the student to become familiar with some of the mathematics necessary for Quantum mechanics before being exposed to the more challenging fundamental concepts.
Special features of the Text:
Quantum chemistry and Quantum physics are presented in a balanced approach.
A strong focus is placedon optical properties of solids. Students will be especially interested on the coverage of color which answers everyday Questions from why the sky is blue to why the grass is green.
Actual engineering applications are used frequently to show students the importance of the developments of math physics.
Other texts available in the MIT Series:
THERMODYNAMICS OF MATERIALS, VOL I, Ragone, 30885-4
THERMODYNAMICS OF MATERIALS, VOL II: KINETICS, Ragone, 30886-2
PHYSICAL CERAMICS: PRINCIPLES FOR CERAMIC SCIENCE AND ENGINEERING, Chiang, Birnie, Kingery, 59873-9
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Topology and Geometry for Physics
A concise but self-contained introduction of the central concepts of modern topology and differential geometry on a mathematical level is given specifically with applications in physics in mind. All basic concepts are systematically provided including sketches of the proofs of most statements.
Smooth finite-dimensional manifolds, tensor and exterior calculus operating on them, homotopy, (co)homology theory including Morse theory of critical points, as well as the theory of fiber bundles and Riemannian geometry, are treated. Examples from physics comprise topological charges, the topology of periodic boundary conditions for solids, gauge fields, geometric phases in quantum physics and gravitation.
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An Invitation to Quantum Groups and Duality
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The Physics of Quantum Fields
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Stanford Course - Modern Physics - Special Relativity
Genre: Physics
"This course is comprised of a six-quarter sequence of classes that will explore the essential theoretical foundations of modern physics. The topics covered in this course sequence will include classical mechanics, quantum mechanics, the general and special theories of relativity, electromagnetism, cosmology, and black holes. While these courses will build upon one another, each course also stands on its own, and both individually and collectively they will let students attain the "theoretical minimum" for thinking intelligently about modern physics. Quantum theory governs the universe at its most basic level. In the first half of the 20th century physics was turned on its head by the radical discoveries of Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg, and Erwin Schroedinger. An entire new logical and mathematical foundation
Modern canonical quantum general relativity
Since matter is described by quantum theory which in turn couples to geometry, we need a quantum theory of gravity. In order to construct quantum gravity one must reformulate quantum theory on a background independent way. Modern Canonical Quantum General Relativity provides a complete treatise of the canonical quantisation of general relativity. The focus is on detailing the conceptual and mathematical framework, on describing physical applications and on summarising the status of this programme in its most popular incarnation, called loop quantum gravity. Mathematical concepts and their relevance to physics are provided within this book, which therefore can be read by graduate students with basic knowledge of quantum field theory or general relativity.
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Quantum Field Theory (Second edition)
Following on from the successful first (1984) and revised (1993) editions, this extended and revised text is designed as a short and simple introduction to quantum field theory for final year physics students and for postgraduate students beginning research in theoretical and experimental particle physics.
The three main objectives of the book are to:
Explain the basic physics and formalism of quantum field theory
To make the reader proficient in theory calculations using Feynman diagrams
To introduce the reader to gauge theories, which play a central role in elementary particle physics.
Thus, the first ten chapters deal with QED in the canonical formalism, and are little changed from the first edition. A brief introduction to gauge theories (Chapter 11) is then followed by two sections, which may be read independently of each other. They cover QCD and related topics (Chapters 12-15) and the unified electroweak theory (Chapters 16
Related Posts Infinite Dimensional Groups and Algebras in Quantum Physics:
- Quantum Probability And Infinite Dimensional Analysis From Foundations To Applications
- Finite or Infinite Dimensional Complex Analysis
- Lie Groups Lie Algebras and Their Representation
- Operator Algebras and Quantum Statistical Mechanics 2 Equilibrium States by Ola Bratteli
- An Invitation to Quantum Groups and Duality
- Lie Algebras in Particle Physics
- Quantum Independent Increment Processes II Structure of Quantum Levy Processes Classical Probability and Physics
- Operators and Representation Theory Canonical Models for Algebras of Operators Arising in Quantum Mechanics
- The Physics of Quantum Fields
- Quantum Physics For Dummies
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