Quantum Geometry Matrix Theory And Gravity
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Quantum Geometry Matrix Theory And Gravity
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Author : Harold C. Steinacker
language : en
Publisher: Cambridge University Press
Release Date : 2024-04-30
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 2024-04-30 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.
Elementary Introduction To Quantum Geometry
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Author : Jan Ambjorn
language : en
Publisher: CRC Press
Release Date : 2022-11-02
Elementary Introduction To Quantum Geometry written by Jan Ambjorn and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-02 with Mathematics categories.
This graduate textbook provides an introduction to quantum gravity, when spacetime is two-dimensional. The quantization of gravity is the main missing piece of theoretical physics, but in two dimensions it can be done explicitly with elementary mathematical tools, but it still has most of the conceptional riddles present in higher dimensional (not yet known) quantum gravity. It provides an introduction to a very interdisciplinary field, uniting physics (quantum geometry) and mathematics (combinatorics) in a non-technical way, requiring no prior knowledge of quantum field theory or general relativity. Using the path integral, the chapters provide self-contained descriptions of random walks, random trees and random surfaces as statistical systems where the free relativistic particle, the relativistic bosonic string and two-dimensional quantum gravity are obtained as scaling limits at phase transition points of these statistical systems. The geometric nature of the theories allows one to perform the path integral by counting geometries. In this way the quantization of geometry becomes closely linked to the mathematical fields of combinatorics and probability theory. By counting the geometries, it is shown that the two-dimensional quantum world is fractal at all scales unless one imposes restrictions on the geometries. It is also discussed in simple terms how quantum geometry and quantum matter can interact strongly and change the properties both of the geometries and of the matter systems. It requires only basic undergraduate knowledge of classical mechanics, statistical mechanics and quantum mechanics, as well as some basic knowledge of mathematics at undergraduate level. It will be an ideal textbook for graduate students in theoretical and statistical physics and mathematics studying quantum gravity and quantum geometry. Key features: Presents the first elementary introduction to quantum geometry Explores how to understand quantum geometry without prior knowledge beyond bachelor level physics and mathematics. Contains exercises, problems and solutions to supplement and enhance learning
New Advances In Quantum Geometry
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Author : Shi-Dong Liang
language : en
Publisher: Mdpi AG
Release Date : 2023-09-28
New Advances In Quantum Geometry written by Shi-Dong Liang and has been published by Mdpi AG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-28 with Science categories.
This special issue contains original research papers and review articles on the subject of Quantum Geometry, a field that attempts to merge the geometric description of gravity, provided by Einstein's theory of general relativity, with the quantum mechanical description of the microscopic world. Diverse approaches are represented, including loop quantum gravity, matrix models, noncommutative geometry and modified gravity theories, together with other, less mainstream models.
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.
Progress In Group Field Theory And Related Quantum Gravity Formalisms
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Author : Steffen Gielen
language : en
Publisher: MDPI
Release Date : 2020-07-01
Progress In Group Field Theory And Related Quantum Gravity Formalisms written by Steffen Gielen and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-01 with Mathematics categories.
Following the fundamental insights from quantum mechanics and general relativity, geometry itself should have a quantum description; the search for a complete understanding of this description is what drives the field of quantum gravity. Group field theory is an ambitious framework in which theories of quantum geometry are formulated, incorporating successful ideas from the fields of matrix models, ten-sor models, spin foam models and loop quantum gravity, as well as from the broader areas of quantum field theory and mathematical physics. This special issue collects recent work in group field theory and these related approaches, as well as other neighbouring fields (e.g., cosmology, quantum information and quantum foundations, statistical physics) to the extent that these are directly relevant to quantum gravity research.
Progress In Group Field Theory And Related Quantum Gravity Formalisms
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Author : Steffen Gielen
language : en
Publisher:
Release Date : 2020
Progress In Group Field Theory And Related Quantum Gravity Formalisms written by Steffen Gielen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
Following the fundamental insights from quantum mechanics and general relativity, geometry itself should have a quantum description; the search for a complete understanding of this description is what drives the field of quantum gravity. Group field theory is an ambitious framework in which theories of quantum geometry are formulated, incorporating successful ideas from the fields of matrix models, ten-sor models, spin foam models and loop quantum gravity, as well as from the broader areas of quantum field theory and mathematical physics. This special issue collects recent work in group field theory and these related approaches, as well as other neighbouring fields (e.g., cosmology, quantum information and quantum foundations, statistical physics) to the extent that these are directly relevant to quantum gravity research.
Quantum Mechanics In The Geometry Of Space Time
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Author : Roger Boudet
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-13
Quantum Mechanics In The Geometry Of Space Time written by Roger Boudet 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 2011-06-13 with Science categories.
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.
Elementary Introduction To Quantum Geometry
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Author : Jan Ambjorn
language : en
Publisher:
Release Date : 2022
Elementary Introduction To Quantum Geometry written by Jan Ambjorn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Geometric quantization categories.
This graduate textbook provides an introduction to quantum gravity, when spacetime is two-dimensional. The quantization of gravity is the main missing piece of theoretical physics, but in two dimensions it can be done explicitly with elementary mathematical tools, but it still has most of the conceptional riddles present in higher dimensional (not yet known) quantum gravity. It provides an introduction to a very interdisciplinary field, uniting physics (quantum geometry) and mathematics (combinatorics) in a non-technical way, requiring no prior knowledge of quantum field theory or general relativity. Using the path integral, the chapters provide self-contained descriptions of random walks, random trees and random surfaces as statistical systems where the free relativistic particle, the relativistic bosonic string and two-dimensional quantum gravity are obtained as scaling limits at phase transition points of these statistical systems. The geometric nature of the theories allows one to perform the path integral by counting geometries. In this way the quantization of geometry becomes closely linked to the mathematical fields of combinatorics and probability theory. By counting the geometries, it is shown that the two-dimensional quantum world is fractal at all scales unless one imposes restrictions on the geometries. It is also discussed in simple terms how quantum geometry and quantum matter can interact strongly and change the properties both of the geometries and of the matter systems. It requires only basic undergraduate knowledge of classical mechanics, statistical mechanics and quantum mechanics, as well as some basic knowledge of mathematics at undergraduate level. It will be an ideal textbook for graduate students in theoretical and statistical physics and mathematics studying quantum gravity and quantum geometry. Key features: Presents the first elementary introduction to quantum geometry Explores how to understand quantum geometry without prior knowledge beyond bachelor level physics and mathematics. Contains exercises, problems and solutions to supplement and enhance learning
Lectures On Matrix Field Theory
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Author : Badis Ydri
language : en
Publisher: Springer
Release Date : 2016-11-22
Lectures On Matrix Field Theory written by Badis Ydri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-22 with Science categories.
These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries. The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is treated in great detail, with a separate chapter on the multitrace approach. The last chapter offers a general introduction to non-commutative gauge theories, while two appendices round out the text. Primarily written as a self-study guide for postgraduate students – with the aim of pedagogically introducing them to key analytical and numerical tools, as well as useful physical models in applications – these lecture notes will also benefit experienced researchers by providing a reference guide to the fundamentals of non-commutative field theory with an emphasis on matrix models and fuzzy geometries.