Quantum Geometry
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Quantum Geometry
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Author : Jan Ambjørn
language : en
Publisher: Cambridge University Press
Release Date : 1997-06-19
Quantum Geometry written by Jan Ambjørn and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-19 with Science categories.
Describes random geometry and applications to strings, quantum gravity, topological field theory and membrane physics.
Quantum Geometry Matrix Theory And Gravity
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Author : Harold C. Steinacker
language : en
Publisher: Cambridge University Press
Release Date : 2024-04-11
Quantum Geometry Matrix Theory And Gravity written by Harold C. Steinacker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-11 with Science categories.
This book describes quantum geometry in the framework of Matrix Theory, which offers a quantum theory of space-time and matter.
M Theory And Quantum Geometry
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Author : Lárus Thorlacius
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
M Theory And Quantum Geometry written by Lárus Thorlacius and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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 quantization of geometrical objects. The majority of lectures at the Advanced Study Institute on Quantum Ge ometry in Akureyri was on recent advances in superstring theory, which is the leading candidate for a unified description of all known elementary par ticles and interactions. The geometric concept of one-dimensional extended objects, or strings, has always been at the core of superstring theory but in recent years the focus has shifted to include also higher-dimensional ob jects, so called D-branes, which play a key role in the non-perturbative dynamics of the theory. A related development has seen the strong coupling regime of a given string theory identified with the weak coupling regime of what was previ ously believed to be a different theory, and a web of such" dualities" that interrelates all known superstring theories has emerged. The resulting uni fied theoretical framework, termed M-theory, has evolved at a rapid pace in recent years.
Geometry Topology And Quantization
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Author : P. Bandyopadhyay
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-10-31
Geometry Topology And Quantization written by P. Bandyopadhyay and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-10-31 with Science categories.
This is a monograph on geometrical and topological features which arise in various quantization procedures. Quantization schemes consider the feasibility of arriving at a quantum system from a classical one and these involve three major procedures viz. i) geometric quantization, ii) Klauder quantization, and iii) stochastic quanti zation. In geometric quantization we have to incorporate a hermitian line bundle to effectively generate the quantum Hamiltonian operator from a classical Hamil tonian. Klauder quantization also takes into account the role of the connection one-form along with coordinate independence. In stochastic quantization as pro posed by Nelson, Schrodinger equation is derived from Brownian motion processes; however, we have difficulty in its relativistic generalization. It has been pointed out by several authors that this may be circumvented by formulating a new geometry where Brownian motion proceses are considered in external as well as in internal space and, when the complexified space-time is considered, the usual path integral formulation is achieved. When this internal space variable is considered as a direc tion vector introducing an anisotropy in the internal space, we have the quantization of a Fermi field. This helps us to formulate a stochastic phase space formalism when the internal extension can be treated as a gauge theoretic extension. This suggests that massive fermions may be considered as Skyrme solitons. The nonrelativistic quantum mechanics is achieved in the sharp point limit.
Multivariate Calculus And Geometry Concepts
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Author : Chirag Verma
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Multivariate Calculus And Geometry Concepts written by Chirag Verma and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Multivariate Calculus and Geometry Concepts" is a comprehensive textbook designed to provide students, researchers, and practitioners with a thorough understanding of fundamental concepts, techniques, and applications in multivariate calculus and geometry. Authored by experts, we offer a balanced blend of theoretical foundations, practical examples, and computational methods, making it suitable for both classroom instruction and self-study. We cover a wide range of topics, including partial derivatives, gradients, line and surface integrals, parametric equations, polar coordinates, conic sections, and differential forms. Each topic is presented clearly and concisely, with detailed explanations and illustrative examples to aid understanding. Our emphasis is on developing a conceptual understanding of key concepts and techniques, rather than rote memorization of formulas. We include numerous figures, diagrams, and geometric interpretations to help readers visualize abstract mathematical concepts and their real-world applications. Practical applications of multivariate calculus and geometry are highlighted throughout the book, with examples drawn from physics, engineering, computer graphics, and other fields. We demonstrate how these concepts are used to solve real-world problems and inspire readers to apply their knowledge in diverse areas. We discuss computational methods and numerical techniques used in multivariate calculus and geometry, such as numerical integration, optimization algorithms, and finite element methods. Programming exercises and computer simulations provide hands-on experience with implementing and applying these methods. Our supplementary resources include online tutorials, solution manuals, and interactive simulations, offering additional guidance, practice problems, and opportunities for further exploration and self-assessment. "Multivariate Calculus and Geometry Concepts" is suitable for undergraduate and graduate students in mathematics, engineering, physics, computer science, and related disciplines. It also serves as a valuable reference for researchers, educators, and professionals seeking a comprehensive overview of multivariate calculus and geometry and its applications in modern science and technology.
Quantum Geometry
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Author : Margaret Prugovecki
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Quantum Geometry written by Margaret Prugovecki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Science categories.
This monograph presents a review and analysis of the main mathematical, physical and epistomological difficulties encountered at the foundational level by all the conventional formulations of relativistic quantum theories, ranging from relativistic quantum mechanics and quantum field theory in Minkowski space, to the various canonical and covariant approaches to quantum gravity. It is, however, primarily devoted to the systematic presentation of a quantum framework meant to deal effectively with these difficulties by reconsidering the foundations of these subjects, analyzing their epistemic nature, and then developing mathematical tools which are specifically designed for the elimination of all the basic inconsistencies. A carefully documented historical survey is included, and additional extensive notes containing quotations from original sources are incorporated at the end of each chapter, so that the reader will be brought up-to-date with the very latest developments in quantum field theory in curved spacetime, quantum gravity and quantum cosmology. The survey further provides a backdrop against which the new foundational and mathematical ideas of the present approach to these subjects can be brought out in sharper relief.
Fractal Geometry And Applications A Jubilee Of Benoit Mandelbrot
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Author : Michel Laurent Lapidus
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Fractal Geometry And Applications A Jubilee Of Benoit Mandelbrot written by Michel Laurent Lapidus and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.
Geometry Of Pdes And Mechanics
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Author : Agostino Prastaro
language : en
Publisher: World Scientific
Release Date : 1996-06-20
Geometry Of Pdes And Mechanics written by Agostino Prastaro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-06-20 with Science categories.
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.
The Universe
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Author : Naresh Dadhich
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Universe written by Naresh Dadhich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
It is with great joy that we present a collection of essays written in honour of Jayant Vishnu Narlikar, who completed 60 years of age on July 19, 1998, by his friends and colleagues, including several of his for mer students. Jayant has had a long research career in astrophysics and cosmology, which he began at Cambridge in 1960, as a student of Sir Fred Hoyle. He started his work with a big bang, expounding on the steady state theory of the Universe and creating a new theory of gravity inspired by Mach's principle. He also worked on action-at-a-distance electrodynamics, inspired by the explorations of Wheeler, Feynman and Hogarth in that direction. This body of work established Jayant's rep utation as a bold and imaginative physicist who was ever willing to take a fresh look at fundamental issues, undeterred by conventional wis dom. This trait, undoubtedly inherited from his teacher and mentor, has always remained with Jayant. It is now most evident in his untir ing efforts to understand anomalies in quasar astronomy, and to develop the quasi-steady state cosmology, along with a group of highly distin guished astronomers including Halton Arp, Geoffrey Burbidge and Fred Hoyle. In spite of all this iconoclastic activity, Jayant remains a part of the mainstream; he appreciates as well as encourages good work along conventional lines by his students and colleagues. This is clear from the range of essays included in this volume, and the variety and distribution of the essayists.
Time Reborn
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Author : Lee Smolin
language : en
Publisher: Knopf Canada
Release Date : 2013-04-23
Time Reborn written by Lee Smolin and has been published by Knopf Canada this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-23 with Science categories.
Since the ancients, physicists have argued that time is not real, that we may think we experience time passing but it's just a human illusion in a timeless universe operating on predetermined laws. Lee brilliantly shows how this thinking came about from our deep need for stability and the eternal, but that indeed time may be the only thing that is real. Since the ancients, physicists have argued that time is not real, that we may think we experience time passing but it's just a human illusion in a timeless universe operating on predetermined laws. Lee brilliantly shows how this thinking came about from our deep need for stability and the eternal, but that indeed time may be the only thing that is real.