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Tensorial Methods and Renormalization in Group Field Theories

2014-04-12 Science
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Release : 2014-04-12
Genre : Science
Kind : eBook
Book Rating : 673/5 ( reviews)

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Book Synopsis Tensorial Methods and Renormalization in Group Field Theories by : Sylvain Carrozza

Download or read book Tensorial Methods and Renormalization in Group Field Theories written by Sylvain Carrozza. This book was released on 2014-04-12. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Tensor Network Contractions

2020-01-27 Science
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Release : 2020-01-27
Genre : Science
Kind : eBook
Book Rating : 894/5 ( reviews)

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Book Synopsis Tensor Network Contractions by : Shi-Ju Ran

Download or read book Tensor Network Contractions written by Shi-Ju Ran. This book was released on 2020-01-27. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Progress in Group Field Theory and Related Quantum Gravity Formalisms

2020-07-01 Mathematics
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Release : 2020-07-01
Genre : Mathematics
Kind : eBook
Book Rating : 783/5 ( reviews)

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Book Synopsis Progress in Group Field Theory and Related Quantum Gravity Formalisms by : Steffen Gielen

Download or read book Progress in Group Field Theory and Related Quantum Gravity Formalisms written by Steffen Gielen. This book was released on 2020-07-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Exact Renormalization Group, The - Proceedings Of The Workshop

1999-08-13
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Release : 1999-08-13
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Kind : eBook
Book Rating : 578/5 ( reviews)

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Book Synopsis Exact Renormalization Group, The - Proceedings Of The Workshop by : Alexander Krasnitz

Download or read book Exact Renormalization Group, The - Proceedings Of The Workshop written by Alexander Krasnitz. This book was released on 1999-08-13. Available in PDF, EPUB and Kindle. Book excerpt: The subject of the exact renormalization group started from pioneering work by Wegner and Houghton in the early seventies and, a decade later, by Polchinski, who formulated the Wilson renormalization group for field theory. In the past decade considerable progress has been made in this field, which includes the development of alternative formulations of the approach and of powerful techniques for solving the exact renormalization group equations, as well as widening of the scope of the exact renormalization group method to include fermions and gauge fields. In particular, two very recent results, namely the manifestly gauge-invariant formulation of the exact renormalization group equation and the proof of the c-theorem in four dimensions, are presented in this volume.

Random Tensors

2017 Mathematics
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Release : 2017
Genre : Mathematics
Kind : eBook
Book Rating : 936/5 ( reviews)

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Book Synopsis Random Tensors by : Razvan Gurau

Download or read book Random Tensors written by Razvan Gurau. This book was released on 2017. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces "Random Tensors," a framework for studying random geometries in any dimension. It provides a complete derivation of the key results in the field. Whatever form a theory of Quantum Gravity may take, it must incorporate random geometry.

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