Random Surfaces And 2d Quantum Gravity
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| Author | : David J Gross |
| Publisher | : World Scientific |
| Total Pages | : 256 |
| Release | : 1991-12-17 |
| Genre | : |
| ISBN | : 9814556300 |
In the past few years there has been much study of random two dimensional surfaces. These provide simple models of string theories with a few degrees of freedom, as well as toy models of quantum gravity. They have possible applications to the statistical mechanics of phase boundaries and to the development of an effective string description of QCD.Recently, methods have been developed to treat these theories nonperturbatively, based on discrete triangulations of the surfaces that can be generated by simple matrix models. Exact solutions with a rich mathematical structure have emerged. All these matters are discussed fully in this book.
| Author | : Orlando Alvarez |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 401 |
| Release | : 2013-03-09 |
| Genre | : Science |
| ISBN | : 146153772X |
The Cargese Workshop Random Surfaces and Quantum Gravity was held from May 27 to June 2, 1990. Little was known about string theory in the non-perturbative regime before Oetober 1989 when non-perturbative equations for the string partition functions were found by using methods based on the random triangulations of surfaees. This set of methods pro vides a deseription of non-eritical string theory or equivalently of the coupling of matter fields to quantum gravity in two dimensions. The Cargese meeting was very successful in that it provided the first opportunity to gather most of the active workers in the field for a fuH week of lectures and extensive informal discussions about these exeiting new developments. The main results were reviewed, recent advances were explained, new results and conjectures (which appear for the first time in these proceedings) were presented and discussed. Among the most important topics discussed at the workshop were: The relation of KdV theory to loop equations and the Virasoro algebra, new results in Liouville field theory, effective (1 + 1) dimensional theory for 2 - D quantum gravity coupled to c = 1 matter and its fermionization, proposal for a new geometrical interpretation of the string equation and possible definition of quantum Riemann surfaces, discussion of the string equation for the multi-matrix models, links with topological field theories of gravity, issues in using target space supersymmetry to define good theories, definition of the partition function via analytic continuation, new models of random surfaces
| Author | : Édouard Brezin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 519 |
| Release | : 2006-07-03 |
| Genre | : Science |
| ISBN | : 140204531X |
Random matrices are widely and successfully used in physics for almost 60-70 years, beginning with the works of Dyson and Wigner. Although it is an old subject, it is constantly developing into new areas of physics and mathematics. It constitutes now a part of the general culture of a theoretical physicist. Mathematical methods inspired by random matrix theory become more powerful, sophisticated and enjoy rapidly growing applications in physics. Recent examples include the calculation of universal correlations in the mesoscopic system, new applications in disordered and quantum chaotic systems, in combinatorial and growth models, as well as the recent breakthrough, due to the matrix models, in two dimensional gravity and string theory and the non-abelian gauge theories. The book consists of the lectures of the leading specialists and covers rather systematically many of these topics. It can be useful to the specialists in various subjects using random matrices, from PhD students to confirmed scientists.
| Author | : Edouard Brezin |
| Publisher | : World Scientific |
| Total Pages | : 1149 |
| Release | : 1993-08-31 |
| Genre | : Science |
| ISBN | : 981450663X |
This book contains an edited comprehensive collection of reprints on the subject of the large N limit as applied to a wide spectrum of problems in quantum field theory and statistical mechanics. The topics include (1) Spin Systems; (2) Large N Limit of Gauge Theories; (3) Two-Dimensional QCD; (4) Exact Results on Planar Perturbation Series and the Nature of the 1/N Series; (5) Schwinger-Dyson Equations Approach; (6) QCD Phenomenological Lagrangians and the Large N Limit; (7) Other Approaches to Large N: Eguchi-Kawai Model, Collective Fields and Numerical Methods; (8) Matrix Models; (9) Two-Dimensional Gravity and String Theory.
| Author | : E. Abdalla |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 325 |
| Release | : 2008-10-04 |
| Genre | : Science |
| ISBN | : 3540483365 |
A comprehensive survey of the use of the Liouville (and super-Liouville) equation in (super)string theory outside the critical dimension, and of the complementary approach based on the discretized space-time - known as the matrix model approach. The authors pay particular attention to supersymmetry, both in the continuum formulation and through the consideration of the super-eigenvalue problem. The methods presented here are important in a large number of complex problems, e.g. random surfaces, 2-D gravity and large-N quantum chromodynamics, and this comparitive study of the different methods permits a cross-evaluation of the results when both methods are valid, combined with new predictions when only one of the methods may be applied.
| Author | : Isaak Markovich Khalatnikov |
| Publisher | : World Scientific |
| Total Pages | : 802 |
| Release | : 1996 |
| Genre | : Science |
| ISBN | : 9789810222536 |
The Landau Institute for Theoretical Physics was created in 1965 by a group of LD Landau's pupils. Very soon, it was widely recognized as one of the world's leading centers in theoretical physics. According to Science Magazine, the Institute in the eighties had the highest citation index among all the scientific organizations in the former Soviet Union. This collection of the best papers of the Institute reflects the development of the many directions in the exact sciences during the last 30 years. The reader can find the original formulations of well-known notions in condensed matter theory, quantum field theory, mathematical physics and astrophysics, which were introduced by members of the Landau Institute.The following are some of the achievements described in this book: monopoles (A Polyakov), instantons (A Belavin et al.), weak crystallization (S Brazovskii), spin superfluidity (I Fomin), finite band potentials (S Novikov) and paraconductivity (A Larkin, L Aslamasov).
| Author | : Roberto Fernandez |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 446 |
| Release | : 2013-03-14 |
| Genre | : Science |
| ISBN | : 3662028662 |
Simple random walks - or equivalently, sums of independent random vari ables - have long been a standard topic of probability theory and mathemat ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk,were introduced into theoretical polymer physics, and gradu ally came to serve as a paradigm for the general theory of critical phenomena. In the past decade, random-walk expansions have evolved into an important tool for the rigorous analysis of critical phenomena in classical spin systems and of the continuum limit in quantum field theory. Among the results obtained by random-walk methods are the proof of triviality of the cp4 quantum field theo ryin space-time dimension d (::::) 4, and the proof of mean-field critical behavior for cp4 and Ising models in space dimension d (::::) 4. The principal goal of the present monograph is to present a detailed review of these developments. It is supplemented by a brief excursion to the theory of random surfaces and various applications thereof. This book has grown out of research carried out by the authors mainly from 1982 until the middle of 1985. Our original intention was to write a research paper. However, the writing of such a paper turned out to be a very slow process, partly because of our geographical separation, partly because each of us was involved in other projects that may have appeared more urgent.
| Author | : Jose Luis Goity |
| Publisher | : World Scientific |
| Total Pages | : 319 |
| Release | : 2005-08-04 |
| Genre | : Science |
| ISBN | : 9814479896 |
The large Nc limit plays a fundamental role in the study of non-abelian gauge theories such as quantum chromodynamics (QCD). Since its discovery in 1974 by 't Hooft, the 1/Nc expansion has provided crucial insights into the non-perturbative aspects of gauge theories. The expansion implemented at the effective theory level is one of the fundamental tools currently in use in hadronic physics; there are important effects and relations that follow from the 1/Nc expansion, which held remarkably well in the real world with Nc= 3. The 1/Ncexpansion also plays a central role in the recently discovered connections between non-Abelian gauge and string theories, promising new ways to analyze the non-perturbative domain of gauge theories.This volume contains contributions from leading theorists and covers the recent developments in the 1/Nc expansion in QCD. The topics addressed include confinement, AdS/CFT correspondence and the string-QCD connection, topology in large Nc, lattice QCD, and a variety of applications to mesons and baryons.
| Author | : M. Fukugita |
| Publisher | : Elsevier |
| Total Pages | : 699 |
| Release | : 2016-06-03 |
| Genre | : Science |
| ISBN | : 1483278050 |
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.
| Author | : Lárus Thorlacius |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 472 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 940114303X |
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.
