Quantum Triangulations
DOWNLOAD
Download Quantum Triangulations PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Quantum Triangulations book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Quantum Triangulations
DOWNLOAD
Author : Mauro Carfora
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-14
Quantum Triangulations written by Mauro Carfora 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 2012-01-14 with Science categories.
Research on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a way which makes manifest the basic geometric structures of the physical interactions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physical theory to make it more amenable for numerical treatment. The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of cases studies, the connection between triangulated manifolds and quantum physics to the deepest. This volume addresses applied mathematicians and theoretical physicists working in the field of quantum geometry and its applications.
Quantum Triangulations
DOWNLOAD
Author : Mauro Carfora
language : en
Publisher: Springer
Release Date : 2017-11-27
Quantum Triangulations written by Mauro Carfora and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-27 with Science categories.
This book discusses key conceptual aspects and explores the connection between triangulated manifolds and quantum physics, using a set of case studies ranging from moduli space theory to quantum computing to provide an accessible introduction to this topic. Research on polyhedral manifolds often reveals unexpected connections between very distinct aspects of mathematics and physics. In particular, triangulated manifolds play an important role in settings such as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, critical phenomena and complex systems. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is also often a consequence of an underlying structure that naturally calls into play non-trivial aspects of representation theory, complex analysis and topology in a way that makes the basic geometric structures of the physical interactions involved clear. This second edition further emphasizes the essential role that triangulations play in modern mathematical physics, with a new and highly detailed chapter on the geometry of the dilatonic non-linear sigma model and its subtle and many-faceted connection with Ricci flow theory. This connection is treated in depth, pinpointing both the mathematical and physical aspects of the perturbative embedding of the Ricci flow in the renormalization group flow of non-linear sigma models. The geometry of the dilaton field is discussed from a novel standpoint by using polyhedral manifolds and Riemannian metric measure spaces, emphasizing their role in connecting non-linear sigma models’ effective action to Perelman’s energy-functional. No other published account of this matter is so detailed and informative. This new edition also features an expanded appendix on Riemannian geometry, and a rich set of new illustrations to help the reader grasp the more difficult points of the theory. The book offers a valuable guide for all mathematicians and theoretical physicists working in the field of quantum geometry and its applications.
Quantum Triangulations
DOWNLOAD
Author : Mauro Carfora
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-14
Quantum Triangulations written by Mauro Carfora 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 2012-01-14 with Science categories.
Research on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a way which makes manifest the basic geometric structures of the physical interactions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physical theory to make it more amenable for numerical treatment. The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of cases studies, the connection between triangulated manifolds and quantum physics to the deepest. This volume addresses applied mathematicians and theoretical physicists working in the field of quantum geometry and its applications.
Percolation On Triangulations A Bijective Path To Liouville Quantum Gravity
DOWNLOAD
Author : Olivier Bernardi
language : en
Publisher: American Mathematical Society
Release Date : 2023-09-27
Percolation On Triangulations A Bijective Path To Liouville Quantum Gravity written by Olivier Bernardi and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-27 with Mathematics categories.
View the abstract.
The Geometry Of Dynamical Triangulations
DOWNLOAD
Author : Jan Ambjorn
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-17
The Geometry Of Dynamical Triangulations written by Jan Ambjorn 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 2009-02-17 with Science categories.
The express purpose of these lecture notes is to go through some aspects of the simplicial quantum gravity model known as the dynamical triangula tions approach. Emphasis has been on laying the foundations of the theory and on illustrating its subtle and often unexplored connections with many distinct mathematical fields ranging from global Riemannian geometry, to moduli theory, number theory, and topology. Our exposition will concentrate on these points so that graduate students may find in these notes a useful exposition of some of the rigorous results one can -establish in this field and hopefully a source of inspiration for new exciting problems. We try as far as currently possible to expose the interplay between the analytical aspects of dynamical triangulations and the results of Monte Carlo simulations. The techniques described here are rather novel and allow us to address points of current interest in the subject of simplicial quantum gravity while requiring very little in the way of fancy field-theoretical arguments. As a consequence, these notes contain mostly original and until now unpublished material, which will hopefully be of interest both to the expert practitioner and to graduate students entering the field. Among the topics addressed here in considerable detail are the following. (i) An analytical discussion of the geometry of dynamical triangulations in dimensions n == 3 and n == 4.
Simulating Triangulations Graphs Manifolds And Quantum Spacetime
DOWNLOAD
Author : Benedikt Krüger
language : en
Publisher:
Release Date : 2016-09-01
Simulating Triangulations Graphs Manifolds And Quantum Spacetime written by Benedikt Krüger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-01 with categories.
Quantum Geometry
DOWNLOAD
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.
Conversations On Quantum Gravity
DOWNLOAD
Author : Jácome Armas
language : en
Publisher: Cambridge University Press
Release Date : 2021-08-26
Conversations On Quantum Gravity written by Jácome Armas 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 2021-08-26 with Biography & Autobiography categories.
Leading theorists share their important insights into the ongoing quest of theoretical physics to find a quantum theory of gravity.
Quantum Invariants Of Knots And 3 Manifolds
DOWNLOAD
Author : Vladimir G. Turaev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-07-11
Quantum Invariants Of Knots And 3 Manifolds written by Vladimir G. Turaev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-11 with Mathematics categories.
Due to the strong appeal and wide use of this monograph, it is now available in its third revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups.The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space.This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. Contents:Invariants of graphs in Euclidean 3-space and of closed 3-manifoldsFoundations of topological quantum field theoryThree-dimensional topological quantum field theoryTwo-dimensional modular functors6j-symbolsSimplicial state sums on 3-manifoldsShadows of manifolds and state sums on shadowsConstructions of modular categories
On Generalised Statistical Equilibrium And Discrete Quantum Gravity
DOWNLOAD
Author : Isha Kotecha
language : en
Publisher: Springer Nature
Release Date : 2022-01-29
On Generalised Statistical Equilibrium And Discrete Quantum Gravity written by Isha Kotecha and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-29 with Science categories.
Absolute concepts of time and energy are integral to standard thermal physics, but background independent systems are devoid of them. This thesis explores the foundational question of generalising equilibrium statistical mechanics to background independent systems, and applies the resulting formulation to non-perturbative discrete quantum gravity. It offers a discussion of the rich interface of thermal physics and quantum gravity in this context, providing a broad contextualisation of such topics. This work details how standard tools from many-body physics can be generalised to discrete quantum gravity labelled with graph-based, or dual polyhedral, quanta that are common to various approaches like tensorial group field theory, loop quantum gravity, dynamical triangulations and lattice quantum gravity. It provides a systematic investigation, both conceptual and technical, of quantum gravitational Gibbs states, thermofield double vacuum states, and their application in condensate cosmology to probe questions of Big Bang singularity resolution and geometric inflation.