The Geometry Of Dynamical Triangulations

Author : Jan Ambjorn,Mauro Carfora,Annalisa Marzuoli
Publisher : Springer Science & Business Media
Page : 207 pages
File Size : 54,9 Mb
Release : 2009-02-17
Category : Science
ISBN : 9783540694274

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The Geometry of Dynamical Triangulations by Jan Ambjorn,Mauro Carfora,Annalisa Marzuoli Pdf

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 As a consequence, these notes contain mostly original and until now unpublished material, which will hopefully be of interest both to the expert practitioner and to graduate students entering the field.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.

Author : Lárus Thorlacius,Thordur Jonsson
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 55,5 Mb
Release : 2000-09-30
Category : Mathematics
ISBN : 0792364759

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M-Theory and Quantum Geometry by Lárus Thorlacius,Thordur Jonsson Pdf

Papers from an August 1999 NATO Advanced Study Institute held in Iceland report on recent advances in superstring theory, which is the leading candidate for a unified description of all known elementary particles and interactions. Chapters examine D-branes in string theory, moduli spaces of Calaba-Yau compactifications, the matrix model of M-theory, the holographic principle, Born-Infeld actions and D-brane physics, superconformal quantum mechanics and multi-black hole moduli spaces, large-N gauge theories, random surfaces, and Lorentzian and Euclidean quantum gravity. The editors are affiliated with the Science Institute of the University of Iceland. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Lárus Thorlacius,Thordur Jonsson
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401143035

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M-Theory and Quantum Geometry by Lárus Thorlacius,Thordur Jonsson Pdf

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.

Author : Mauro Carfora,Annalisa Marzuoli
Publisher : Springer
Page : 392 pages
File Size : 46,8 Mb
Release : 2017-11-27
Category : Science
ISBN : 9783319679372

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Quantum Triangulations by Mauro Carfora,Annalisa Marzuoli Pdf

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.

Author : John M. Charap
Publisher : Cambridge University Press
Page : 354 pages
File Size : 50,6 Mb
Release : 1995-01-05
Category : Mathematics
ISBN : 0521482712

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Geometry of Constrained Dynamical Systems by John M. Charap Pdf

A lively, varied and topical presentation of this branch of theoretical physics.

Author : Matilde Marcolli
Publisher : MIT Press
Page : 390 pages
File Size : 55,9 Mb
Release : 2020-05-26
Category : Mathematics
ISBN : 9780262358323

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Lumen Naturae by Matilde Marcolli Pdf

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.

Author : Jan Ambjørn,Bergfinnur Durhuus,Þórður Jónsson
Publisher : Cambridge University Press
Page : 377 pages
File Size : 40,5 Mb
Release : 1997-06-19
Category : Science
ISBN : 9780521461672

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Quantum Geometry by Jan Ambjørn,Bergfinnur Durhuus,Þórður Jónsson Pdf

Describes random geometry and applications to strings, quantum gravity, topological field theory and membrane physics.

Author : Gianluca Calcagni,Lefteris Papantonopoulos,George Siopsis,Nikos Tsamis
Publisher : Springer
Page : 402 pages
File Size : 53,6 Mb
Release : 2012-10-31
Category : Science
ISBN : 9783642330360

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Quantum Gravity and Quantum Cosmology by Gianluca Calcagni,Lefteris Papantonopoulos,George Siopsis,Nikos Tsamis Pdf

Quantum gravity has developed into a fast-growing subject in physics and it is expected that probing the high-energy and high-curvature regimes of gravitating systems will shed some light on how to eventually achieve an ultraviolet complete quantum theory of gravity. Such a theory would provide the much needed information about fundamental problems of classical gravity, such as the initial big-bang singularity, the cosmological constant problem, Planck scale physics and the early-time inflationary evolution of our Universe. While in the first part of this book concepts of quantum gravity are introduced and approached from different angles, the second part discusses these theories in connection with cosmological models and observations, thereby exploring which types of signatures of modern and mathematically rigorous frameworks can be detected by experiments. The third and final part briefly reviews the observational status of dark matter and dark energy, and introduces alternative cosmological models. Edited and authored by leading researchers in the field and cast into the form of a multi-author textbook at postgraduate level, this volume will be of benefit to all postgraduate students and newcomers from neighboring disciplines wishing to find a comprehensive guide for their future research.

Author : Astrid Eichhorn,Benjamin Bahr,Antonio D. Pereira
Publisher : Frontiers Media SA
Page : 298 pages
File Size : 48,8 Mb
Release : 2021-07-15
Category : Science
ISBN : 9782889710492

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Coarse Graining in Quantum Gravity: Bridging the Gap between Microscopic Models and Spacetime-Physics by Astrid Eichhorn,Benjamin Bahr,Antonio D. Pereira Pdf

Author : Vladimir G. Ivancevic
Publisher : World Scientific
Page : 855 pages
File Size : 49,5 Mb
Release : 2008
Category : Science
ISBN : 9789812819284

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Quantum Leap by Vladimir G. Ivancevic Pdf

This is a unique 21st-century monograph that reveals a basic, yet deep understanding of the universe, as well as the human mind and body OCo all from the perspective of quantum mechanics and quantum field theory.This book starts with both non-mathematical and mathematical preliminaries. It presents the basics of both non-relativistic and relativistic quantum mechanics, and introduces Feynman path integrals and their application to quantum fields and string theory, as well as some non-quantum applications. It then describes the quantum universe in the form of loop quantum gravity and quantum cosmology. Lastly, the book turns to the human body and mind, applying quantum theory to electro-muscular stimulation and consciousness.It can be used as a graduate (or advanced undergraduate) textbook for a two-semester course in quantum physics and its modern applications. Some parts of the book can also be used by engineers, biologists, psychologists and computer scientists, as well as applied mathematicians, both in industry and academia."

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
Page : 812 pages
File Size : 41,5 Mb
Release : 2007
Category : Mathematics
ISBN : 3037190299

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Handbook of Teichmüller Theory by Athanase Papadopoulos Pdf

The Teichmuller space of a surface was introduced by O. Teichmuller in the 1930s. It is a basic tool in the study of Riemann's moduli spaces and the mapping class groups. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics. The original setting of Teichmuller theory is complex analysis. The work of Thurston in the 1970s brought techniques of hyperbolic geometry to the study of Teichmuller space and its asymptotic geometry. Teichmuller spaces are also studied from the point of view of the representation theory of the fundamental group of the surface in a Lie group $G$, most notably $G=\mathrm{PSL}(2,\mathbb{R})$ and $G=\mathrm{PSL}(2,\mathbb{C})$. In the 1980s, there evolved an essentially combinatorial treatment of the Teichmuller and moduli spaces involving techniques and ideas from high-energy physics, namely from string theory. The current research interests include the quantization of Teichmuller space, the Weil-Petersson symplectic and Poisson geometry of this space as well as gauge-theoretic extensions of these structures. The quantization theories can lead to new invariants of hyperbolic 3-manifolds. The purpose of this handbook is to give a panorama of some of the most important aspects of Teichmuller theory. The handbook should be useful to specialists in the field, to graduate students, and more generally to mathematicians who want to learn about the subject. All the chapters are self-contained and have a pedagogical character. They are written by leading experts in the subject.

Author : Jan Ambjorn
Publisher : CRC Press
Page : 329 pages
File Size : 42,9 Mb
Release : 2022-11-02
Category : Science
ISBN : 9781000776027

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Elementary Introduction to Quantum Geometry by Jan Ambjorn Pdf

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

Author : B. Casciaro,D. Fortunato,M. Francaviglia,A. Masiello
Publisher : Springer Science & Business Media
Page : 521 pages
File Size : 48,7 Mb
Release : 2011-06-28
Category : Science
ISBN : 9788847021136

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Recent Developments in General Relativity by B. Casciaro,D. Fortunato,M. Francaviglia,A. Masiello Pdf

The 13th Italian Conference on General Relativity and Gravitational Physics was held in Cala Corvino-Monopoli (Bari) from September 21to September 25, 1998. The Conference, which is held every other year in different Italian locations, has brought together, as in the earlier conferences in this series, those scientists who are interested and actively work in all aspects of general relativity, from both the mathematical and the physical points of view: from classical theories of gravitation to quantum gravity, from relativistic astrophysics and cosmology to experiments in gravitation. About 70 participants came from Departments of Astronomy and Astrophysics, Departments of Mathematics and Departments of Experimental and Theoretical Physics from all over the Country; in addition a few Italian scientists working abroad kindly accepted invitations from the Scientific Committee. The good wishes of the University and of the Politecnico di Bari were conveyed by the director of Diparti mento Interuniversitario di Matematica, Prof. Franco Altomare. These proceedings contain the contributions of the two winners of the SIGRAV prizes, the invited talks presented at the Conference and most of the contributed talks. We thank all of our colleagues, who did their best to prepare their manuscripts. The pleasant atmosphere induced by the beauty of the place was greatlyenhanced not only by the participation of so many colleagues, who had lively discussions about science well beyond Conference hours, but also by the feeling of hospitalityextended to the participants by the staff of the Cala Corvino Hotel, where the Conference was held.

Author : Edith Falgarone,Thierry Passot
Publisher : Springer Science & Business Media
Page : 484 pages
File Size : 49,6 Mb
Release : 2003-03-11
Category : Science
ISBN : 9783540002741

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Turbulence and Magnetic Fields in Astrophysics by Edith Falgarone,Thierry Passot Pdf

This book contains review articles of most of the topics addressed at the conf- ence on Simulations of Magnetohydrodynamic turbulence in astrophysics: recent achievements and perspectives which took place from July 2 to 6, 2001 at the Institut Henri Poincar ́e in Paris. We made the choice to publish these lectures in a tutorial form so that they can be read by a broad audience. As a result, this book does not give an exhaustive view of all the subjects addressed during the conference. The main objective of this workshop which gathered about 90 scientists from di?erent ?elds, was to present and confront recent results on the topic of t- bulence in magnetized astrophysical environments. A second objective was to discuss the latest generation of numerical codes, such as those using adaptive mesh re?nement (AMR) techniques. During a plenary discussion at the end of the workshop discussions were held on several topics, often at the heart of vivid controversies. Topics included the timescale for the dissipation of magneto-hydrodynamical (MHD) turbulence, the role of boundary conditions, the characteristics of imbalanced turbulence, the validity of the polytropic approach to Alfv ́en waves support within interst- lar clouds, the source of turbulence inside clouds devoid of stellar activity, the timescale for star formation, the Alfv ́en Mach number of interstellar gas motions, the formation process for helical ?elds in the interstellar medium. The impact of small upon large scales was also discussed.

Author : Ion-Olimpiu Stamatescu,Erhard Seiler
Publisher : Springer
Page : 422 pages
File Size : 54,9 Mb
Release : 2007-09-28
Category : Science
ISBN : 9783540711179

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Approaches to Fundamental Physics by Ion-Olimpiu Stamatescu,Erhard Seiler Pdf

This book offers a portrait of the research landscape of present-day fundamental theoretical physics. It presents contributions on particle theory, quantum field theory, general relativity, quantum gravity, string theory and cosmology. The book examines a way of communicating about methods, achievements and promises of the different approaches which shape the development of this field.