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Quantum Triangulations
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Book Synopsis Quantum Triangulations by : Mauro Carfora
Download or read book Quantum Triangulations written by Mauro Carfora and published by Springer Science & Business Media. This book was released on 2012-01-14 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Triangulations by : Mauro Carfora
Download or read book Quantum Triangulations written by Mauro Carfora and published by Springer. This book was released on 2017-11-27 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Geometry of Dynamical Triangulations by : Jan Ambjorn
Download or read book The Geometry of Dynamical Triangulations written by Jan Ambjorn and published by Springer Science & Business Media. This book was released on 2009-02-17 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Invariants of Knots and 3-Manifolds by : Vladimir G. Turaev
Download or read book Quantum Invariants of Knots and 3-Manifolds written by Vladimir G. Turaev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-07-11 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Discrete Causal Theory by : Benjamin F. Dribus
Download or read book Discrete Causal Theory written by Benjamin F. Dribus and published by Springer. This book was released on 2017-04-26 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book evaluates and suggests potentially critical improvements to causal set theory, one of the best-motivated approaches to the outstanding problems of fundamental physics. Spacetime structure is of central importance to physics beyond general relativity and the standard model. The causal metric hypothesis treats causal relations as the basis of this structure. The book develops the consequences of this hypothesis under the assumption of a fundamental scale, with smooth spacetime geometry viewed as emergent. This approach resembles causal set theory, but differs in important ways; for example, the relative viewpoint, emphasizing relations between pairs of events, and relationships between pairs of histories, is central. The book culminates in a dynamical law for quantum spacetime, derived via generalized path summation.
Book Synopsis Selected Works of Oded Schramm by : Itai Benjamini
Download or read book Selected Works of Oded Schramm written by Itai Benjamini and published by Springer Science & Business Media. This book was released on 2011-08-12 with total page 1199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of the late Oded Schramm (1961-2008), distinguished mathematician. Throughout his career, Schramm made profound and beautiful contributions to mathematics that will have a lasting influence. In these two volumes, Editors Itai Benjamini and Olle Häggström have collected some of his papers, supplemented with three survey papers by Steffen Rohde, Häggström and Cristophe Garban that further elucidate his work. The papers within are a representative collection that shows the breadth, depth, enthusiasm and clarity of his work, with sections on Geometry, Noise Sensitivity, Random Walks and Graph Limits, Percolation, and finally Schramm-Loewner Evolution. An introduction by the Editors and a comprehensive bibliography of Schramm's publications complete the volume. The book will be of especial interest to researchers in probability and geometry, and in the history of these subjects.
Download or read book Lattice 91 written by M. Fukugita and published by Elsevier. This book was released on 2016-06-03 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lattice 91 covers the proceedings of the International Symposium on Lattice Field Theory held in Tsukuba, Japan on 5-9 November 1991. The book focuses on quantum chromodynamics, Higgs-fermion theories, QED, lattice quantum gravity and random surfaces, spin systems related to field theory, simulation algorithms, and dedicated computers. The selection first offers information on the QCD spectrum and phase diagram on the lattice and QCD at finite density, including phase structure of QCD, Monte-Carlo simulations with dynamical fermions, and quenched approximation. The book then tackles weak matrix elements, simulation of heavy quarks, and sphaleron induced baryon number non-conservation. The text reviews quantum gravity and random surfaces, recent analytic progress in finite size effects, and parallel QCD machines. Discussions focus on two-dimensional quantum gravity, signatures of resonance in finite volume, first order transitions, and determination of the running coupling. The publication also ponders on hadronic forces from the lattice, universality of the confinement string in multiple potentials, and confinement and saddle-point configurations. The selection is highly recommended for readers interested in the lattice field theory.
Book Synopsis The Twelfth Marcel Grossmann Meeting by : Thibault Damour
Download or read book The Twelfth Marcel Grossmann Meeting written by Thibault Damour and published by World Scientific. This book was released on 2012-02-02 with total page 2660 pages. Available in PDF, EPUB and Kindle. Book excerpt: Marcel Grossmann Meetings are formed to further the development of General Relativity by promoting theoretical understanding in the fields of physics, mathematics, astronomy and astrophysics and to direct future technological, observational, and experimental efforts. In these meetings are discussed recent developments in classical and quantum gravity, general relativity and relativistic astrophysics, with major emphasis on mathematical foundations and physical predictions, with the main objective of gathering scientists from diverse backgrounds for deepening the understanding of spacetime structure and reviewing the status of test-experiments for Einstein's theory of gravitation. The range of topics is broad, going from the more abstract classical theory, quantum gravity and strings, to the more concrete relativistic astrophysics observations and modeling. The three volumes of the proceedings of MG12 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting includes 29 plenary talks stretched over 6 mornings, and 74 parallel sessions over 5 afternoons. Volume A contains plenary and review talks ranging from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theories, to precision tests of general relativity including progress towards the detection of gravitational waves, to relativistic astrophysics including such topics as gamma ray bursts, black hole physics both in our galaxy, in active galactic nuclei and in other galaxies, neutron stars, pulsar astrophysics, gravitational lensing effects, neutrino physics and ultra high energy cosmic rays. The rest of the volumes include parallel sessions on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, binary systems, radiative transfer, accretion disks, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, cosmic background radiation & observational cosmology, numerical relativity & algebraic computing, gravitational lensing, variable “constants” of nature, large scale structure, topology of the universe, brane-world cosmology, early universe models & cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, gamma ray burst modeling, supernovas, global structure, singularities, cosmic censorship, chaos, Einstein–Maxwell systems, inertial forces, gravitomagnetism, wormholes & time machines, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors & data analysis, precision gravitational measurements, history of relativity, quantum gravity & loop quantum gravity, Casimir effect, quantum cosmology, strings & branes, self-gravitating systems, gamma ray astronomy, cosmic rays, gamma ray bursts and quasars. Sample Chapter(s) Space-Time from the Spectral Point of View (467k) Contents: Space-Time from the Spectral Point of View (Ali H Chamseddine and Alain Connes)The Formation of Black Holes in General Relativity (Demetrios Christodoulou)Matching Conditions in Relativistic Astrophysics (Hernando Quevedo)Black Holes as a Source of Information (Juan Maldacena)Black Hole Microstate Counting and Its Macroscopic Counterpart (Ipsita Mandal and Ashoke Sen)Transplanckian String Collisions: An Update (Gabriele Veneziano)Ultraviolet Divergences and Scale-Dependent Gravitational Couplings (Herbert W Hamber)The Black Hole Stability Problem for Linear Scalar Perturbations (Mihalis Dafermos and Igor Rodnianski)The Global Network of Laser Interferometer Gravitational Wave Detectors (David H Reitze)Analytical Relativity of Black Holes (Thibault Damour)Detection of Gravitational Waves Using Pulsar Timing (Richard N Manchester)Relativistic Spin-Precession in Binary Pulsars (Michael Kramer)Supernovae and Gamma-Ray Bursts: 10 Years of Observations (Massimo Della Valle)Gamma-Ray Bursts as Relativistic Objects (Tsvi Piran)Fundamental Physics from Black Holes, Neutron Stars and Gamma-Ray Bursts (Remo Ruffini)The Fascinating TeV Sky (Felix Aharonian)Galaxy Clusters and Their Central Supermassive Black Holes: Case of M87 (Eugene Churazov, Sergey Sazonov, Rashid Sunyaev, William Forman, Christine Jones and Hans Böhringer)Intergalactic Shock Fronts (Maxim Markevitch)Studies of Dark Energy with X-Ray Observations of Galaxy Clusters (Alexey Vikhlinin)and other papers Keywords:General Relativity;Gravitation;Astrophysics;Quantum Gravity;Particle Physics;Cosmology;Theoretical Physics
Book Synopsis Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity by : Olivier Bernardi
Download or read book Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity written by Olivier Bernardi and published by American Mathematical Society. This book was released on 2023-09-27 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Handbook of Teichmüller Theory by : Athanase Papadopoulos
Download or read book Handbook of Teichmüller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this handbook is Teichmuller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with $3$-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas toward a unique subject is a manifestation of the unity and harmony of mathematics. This volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in these fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems. This volume is divided into the following four sections: The metric and the analytic theory The group theory The algebraic topology of mapping class groups and moduli spaces Teichmuller theory and mathematical physics This handbook is addressed to graduate students and researchers in all the fields mentioned.
Book Synopsis Springer Handbook of Spacetime by : Abhay Ashtekar
Download or read book Springer Handbook of Spacetime written by Abhay Ashtekar and published by Springer. This book was released on 2014-09-01 with total page 883 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courses on these subjects. The Handbook is divided into six parts. Part A: Introduction to Spacetime Structure. Part B: Foundational Issues. Part C: Spacetime Structure and Mathematics. Part D: Confronting Relativity theories with observations. Part E: General relativity and the universe. Part F: Spacetime beyond Einstein.
Book Synopsis Handbook of Gravitational Wave Astronomy by : Cosimo Bambi
Download or read book Handbook of Gravitational Wave Astronomy written by Cosimo Bambi and published by Springer Nature. This book was released on 2022-07-02 with total page 1895 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook provides an updated comprehensive description of gravitational wave astronomy. In the first part, it reviews gravitational wave experiments, from ground and space based laser interferometers to pulsar timing arrays and indirect detection from the cosmic microwave background. In the second part, it discusses a number of astrophysical and cosmological gravitational wave sources, including black holes, neutron stars, possible more exotic objects, and sources in the early Universe. The third part of the book reviews the methods to calculate gravitational waveforms. The fourth and last part of the book covers techniques employed in gravitational wave astronomy data analysis. This book represents both a valuable resource for graduate students and an important reference for researchers in gravitational wave astronomy.
Book Synopsis Combinatorics and Physics by : Kurusch Ebrahimi-Fard
Download or read book Combinatorics and Physics written by Kurusch Ebrahimi-Fard and published by American Mathematical Soc.. This book was released on 2011 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the mini-workshop Renormalization, held in December 2006, and the conference Combinatorics and Physics, held in March 2007. Both meetings took place at the Max-Planck-Institut fur Mathematik in Bonn, Germany. Research papers in the volume provide an overview of applications of combinatorics to various problems, such as applications to Hopf algebras, techniques to renormalization problems in quantum field theory, as well as combinatorial problems appearing in the context of the numerical integration of dynamical systems, in noncommutative geometry and in quantum gravity. In addition, it contains several introductory notes on renormalization Hopf algebras, Wilsonian renormalization and motives.
Book Synopsis Path Integrals--New Trends and Perspectives by : Wolfhard Janke
Download or read book Path Integrals--New Trends and Perspectives written by Wolfhard Janke and published by World Scientific. This book was released on 2008 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains selected talks and poster presentations from the 9th International Conference on Path Integrals OCo New Trends and Perspectives, which took place at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, during the period September 23OCo28, 2007. Continuing the well-developed tradition of the conference series, the present status of both the different techniques of path integral calculations and their diverse applications to many fields of physics and chemistry is reviewed. This is reflected in the main topics in this volume, which range from more traditional fields such as general quantum physics and quantum or statistical field theory through technical aspects like Monte Carlo simulations to more modern applications in the realm of quantum gravity and astrophysics, condensed matter physics with topical subjects such as BoseOCoEinstein condensation or quantum wires, biophysics and econophysics. All articles are successfully tied together by the common method of path integration; as a result, special methodological advancements in one topic could be transferred to other topics."
Book Synopsis String Theory For Dummies by : Andrew Zimmerman Jones
Download or read book String Theory For Dummies written by Andrew Zimmerman Jones and published by John Wiley & Sons. This book was released on 2009-11-16 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear, plain-English guide to this complex scientific theory String theory is the hottest topic in physics right now, with books on the subject (pro and con) flying out of the stores. String Theory For Dummies offers an accessible introduction to this highly mathematical "theory of everything," which posits ten or more dimensions in an attempt to explain the basic nature of matter and energy. Written for both students and people interested in science, this guide explains concepts, discusses the string theory's hypotheses and predictions, and presents the math in an approachable manner. It features in-depth examples and an easy-to-understand style so that readers can understand this controversial, cutting-edge theory.
Book Synopsis Featured Reviews in "Mathematical Reviews" 1995-1996 by : Donald G. Babbitt
Download or read book Featured Reviews in "Mathematical Reviews" 1995-1996 written by Donald G. Babbitt and published by American Mathematical Soc.. This book was released on with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of reprinted 'Featured Reviews' published in Mathematical Reviews (MR) in 1995 and 1996 makes widely available informed reviews of some of the best mathematics published recently. 'Featured Reviews' were introduced in MR at the beginning of 1995 in part to provide some guidance to the current research-level literature. With the exponential growth of publications in mathematical research in the first half-century of MR, it had become essentially impossible for users of MR to identify the most important new research-level books and papers, especially in fields outside of the users' own expertise. This work identifies some of the "best" new publications, papers, and books that are expected to have a significant impact on the area of pure or applied mathematics with which researchers are concerned. All of the papers reviewed here contain interesting new ideas or applications, a deep synthesis of existing ideas, or any combination of these. The volume is intended to lead the user to important new research across all fields covered by MR.
Download or read book Lumen Naturae written by Matilde Marcolli and published by MIT Press. This book was released on 2020-05-26 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring common themes in modern art, mathematics, and science, including the concept of space, the notion of randomness, and the shape of the cosmos. This is a book about art—and a book about mathematics and physics. In Lumen Naturae (the title refers to a purely immanent, non-supernatural form of enlightenment), mathematical physicist Matilde Marcolli explores common themes in modern art and modern science—the concept of space, the notion of randomness, the shape of the cosmos, and other puzzles of the universe—while mapping convergences with the work of such artists as Paul Cezanne, Mark Rothko, Sol LeWitt, and Lee Krasner. Her account, focusing on questions she has investigated in her own scientific work, is illustrated by more than two hundred color images of artworks by modern and contemporary artists. Thus Marcolli finds in still life paintings broad and deep philosophical reflections on space and time, and connects notions of space in mathematics to works by Paul Klee, Salvador Dalí, and others. She considers the relation of entropy and art and how notions of entropy have been expressed by such artists as Hans Arp and Fernand Léger; and traces the evolution of randomness as a mode of artistic expression. She analyzes the relation between graphical illustration and scientific text, and offers her own watercolor-decorated mathematical notebooks. Throughout, she balances discussions of science with explorations of art, using one to inform the other. (She employs some formal notation, which can easily be skipped by general readers.) Marcolli is not simply explaining art to scientists and science to artists; she charts unexpected interdependencies that illuminate the universe.
