Tensorial Methods And Renormalization In Group Field Theories
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Tensorial Methods And Renormalization In Group Field Theories
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Author : Sylvain Carrozza
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-04-12
Tensorial Methods And Renormalization In Group Field Theories written by Sylvain Carrozza 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 2014-04-12 with Science categories.
The main focus of this thesis is the mathematical structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related, on the one hand, to Loop Quantum Gravity (LQG) and on the other, to matrix- and tensor models. Background material on these topics, including conceptual and technical aspects, are introduced in the first chapters. The work then goes on to explain how the standard tools of Quantum Field Theory can be generalized to GFTs and exploited to study the large cut-off behaviour and renormalization group transformations of the latter. Among the new results derived in this context are a proof of renormalizability of a three-dimensional GFT with gauge group SU(2), which opens the way to applications of the formalism to quantum gravity.
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.
Coarse Graining In Quantum Gravity Bridging The Gap Between Microscopic Models And Spacetime Physics
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Author : Astrid Eichhorn
language : en
Publisher: Frontiers Media SA
Release Date : 2021-07-15
Coarse Graining In Quantum Gravity Bridging The Gap Between Microscopic Models And Spacetime Physics written by Astrid Eichhorn and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-15 with Science categories.
Combinatorial Physics
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Author : Adrian Tanasa
language : en
Publisher: Oxford University Press
Release Date : 2021
Combinatorial Physics written by Adrian Tanasa and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Computers categories.
The goal of the book is to use combinatorial techniques to solve fundamental physics problems, and vice-versa, to use theoretical physics techniques to solve combinatorial problems.
Introduction To Tensor Network Methods
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Author : Simone Montangero
language : en
Publisher: Springer
Release Date : 2018-11-28
Introduction To Tensor Network Methods written by Simone Montangero and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-28 with Science categories.
This volume of lecture notes briefly introduces the basic concepts needed in any computational physics course: software and hardware, programming skills, linear algebra, and differential calculus. It then presents more advanced numerical methods to tackle the quantum many-body problem: it reviews the numerical renormalization group and then focuses on tensor network methods, from basic concepts to gauge invariant ones. Finally, in the last part, the author presents some applications of tensor network methods to equilibrium and out-of-equilibrium correlated quantum matter. The book can be used for a graduate computational physics course. After successfully completing such a course, a student should be able to write a tensor network program and can begin to explore the physics of many-body quantum systems. The book can also serve as a reference for researchers working or starting out in the field.
Methods In Field Theory Les Houches Session Xxviii
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Author : R Balian
language : en
Publisher: World Scientific
Release Date : 1993-03-31
Methods In Field Theory Les Houches Session Xxviii written by R Balian and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-03-31 with Science categories.
This book is one of the most important reference books in Field Theory with permanent value. To enable wider access by students, researchers and libraries of developing countries, this valuable volume has been reprinted and is sold at a much lower price than before.
Introduction To Quantum Field Theory With Applications To Quantum Gravity
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Author : Iosif L. Buchbinder
language : en
Publisher: Oxford University Press
Release Date : 2021-03-01
Introduction To Quantum Field Theory With Applications To Quantum Gravity written by Iosif L. Buchbinder and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-01 with Science categories.
Applications of quantum field theoretical methods to gravitational physics, both in the semiclassical and the full quantum frameworks, require a careful formulation of the fundamental basis of quantum theory, with special attention to such important issues as renormalization, quantum theory of gauge theories, and especially effective action formalism. The first part of this graduate textbook provides both a conceptual and technical introduction to the theory of quantum fields. The presentation is consistent, starting from elements of group theory, classical fields, and moving on to the effective action formalism in general gauge theories. Compared to other existing books, the general formalism of renormalization in described in more detail, and special attention paid to gauge theories. This part can serve as a textbook for a one-semester introductory course in quantum field theory. In the second part, we discuss basic aspects of quantum field theory in curved space, and perturbative quantum gravity. More than half of Part II is written with a full exposition of details, and includes elaborated examples of simplest calculations. All chapters include exercises ranging from very simple ones to those requiring small original investigations. The selection of material of the second part is done using the “must-know” principle. This means we included detailed expositions of relatively simple techniques and calculations, expecting that the interested reader will be able to learn more advanced issues independently after working through the basic material, and completing the exercises.
Nuclear Science Abstracts
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Author :
language : en
Publisher:
Release Date : 1976-06
Nuclear Science Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-06 with Nuclear energy categories.
New Problems Methods And Techniques In Quantum Field Theory And Statistical Mechanics
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Author : Mario Rasetti
language : en
Publisher: World Scientific
Release Date : 1990
New Problems Methods And Techniques In Quantum Field Theory And Statistical Mechanics written by Mario Rasetti and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Science categories.
http://www.worldscientific.com/worldscibooks/10.1142/1095
Tensor Network Contractions
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Author : Shi-Ju Ran
language : en
Publisher: Springer Nature
Release Date : 2020-01-27
Tensor Network Contractions written by Shi-Ju Ran and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-27 with Science categories.
Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.