Download or read book Random Surfaces and Quantum Gravity written by Orlando Alvarez and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Random Surfaces and 2D Quantum Gravity written by Spain) Workshop on Random Surfaces and 2D Quantum Gravity (1991 : Barcelana and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Two Dimensional Quantum Gravity And Random Surfaces 8th Jerusalem Winter School For Theoretical Physics written by David J Gross and published by World Scientific. This book was released on 1991-12-17 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Two Dimensional Quantum Gravity and Random Surfaces written by David Gross and published by . This book was released on 1992 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Two Dimensional Quantum Gravity and Random Surfaces written by David J. Gross and published by . This book was released on 1992 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Random Surface Interpretations of Two dimensional Liouville Quantum Gravity and Yang Mills Theory written by Minjae Park (Scientist in mathematics) and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The theory of random surfaces (or "sums over surfaces") has its historical roots in quantum gravity, string theory, statistical physics, and combinatorics. This thesis explores random surfaces in two settings: one related to Liouville quantum gravity, and one related to Euclidean Yang-Mills theory in two dimensions." "The first part introduces a specific regularization of Liouville quantum gravity surfaces. It also establishes the Polyakov-Alvarez formula on non-smooth surfaces with Brownian loops instead of the zeta-regularized Laplacian determinant. Consequently, "weighting by a Brownian loop soup" changes the so-called central charge of the regularized random surfaces, as expected in physic literature. This result justifies a definition of Liouville quantum gravity surfaces in the supercritical regime where the central charge is greater than 1." The second part describes continuum Wilson loop expectations on the plane as sums over surfaces, an example of gauge string duality. In contrast to the Gross-Taylor expansion, our weight is explicit as ±N[superscript [chi]] where [chi] is the Euler characteristic, for any gauge group U(N), SO(N), Sp(N/2). Based on the well-established continuum theory in two dimensions, we provide a probabilistic treatment for Wilson loop expectations, also leading to various applications like an alternative proof for the Makeenko-Migdal equation and a connection with a random walk on permutations.

Download or read book Random Surfaces written by Scott Sheffield and published by . This book was released on 2005 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Random Surfaces and 2D Quantum Gravity Proceedings of the Workshop 1991 Barcelona Spain written by J....[et al] Ambjørn and published by . This book was released on 1992 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Random Surfaces and 2D Quantum Gravity written by Jan Ambjørn and published by . This book was released on 1992 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Regularized Quantum Gravity and String Theory written by J. (Kbh. Univ. Niels Bohr Institutet) Ambjørn and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Random Surfaces written by Martin Guy Harris and published by . This book was released on 1994 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Random Surfaces and 2D Quantum Gravity written by J Ambjorn and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Elementary Introduction to Quantum Geometry written by Jan Ambjorn and published by CRC Press. This book was released on 2022-11-02 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book A New Approach to Three dimensional Quantum Gravity written by J. (Kbh. Univ. Niels Bohr Institutet) Ambjørn and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Quantum Geometry written by Jan Ambjørn and published by Cambridge University Press. This book was released on 1997-06-19 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes random geometry and applications to strings, quantum gravity, topological field theory and membrane physics.

Download or read book Probabilistic Methods in Quantum Field Theory and Quantum Gravity written by Poul Henrik Damgaard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: From August 21 through August 27, 1989 the Nato Advanced Research Workshop Probabilistic Methods in Quantum Field Theory and Quantum Gravity" was held at l'Institut d'Etudes Scientifiques, Cargese, France. This publication is the Proceedings of this workshop. The purpose of the workshop was to bring together a group of scientists who have been at the forefront of the development of probabilistic methods in Quantum Field Theory and Quantum Gravity. The original thought was to put emphasis on the introduction of stochastic processes in the understanding of Euclidean Quantum Field Theory, with also some discussion of recent progress in the field of stochastic numerical methods. During the final preparation of the meeting we broadened the scope to include all those Euclidean Quantum Field Theory descriptions that make direct reference to concepts from probability theory and statistical mechanics. Several of the main contributions centered around a more rigorous discussion of stochastic processes for the formulation of Euclidean Quantum Field Theory. These rather stringent mathematical approaches were contrasted with the more heuristic stochastic quantization scheme developed in 1981 by Parisi and Wu: Stochastic quan tization, its intrinsic BRST -structure and stochastic regularization appeared in many disguises and in connection with several different problems throughout the workshop.

Download or read book Quantum Geometry written by Jan Ambjørn and published by Cambridge University Press. This book was released on 2005-12-15 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate level text describes in a unified fashion the statistical mechanics of random walks, random surfaces and random higher dimensional manifolds with an emphasis on the geometrical aspects of the theory and applications to the quantization of strings, gravity and topological field theory. With chapters on random walks, random surfaces, two-and higher-dimensional quantum gravity, topological quantum field theories and Monte Carlo simulations of random geometries, the text provides a self-contained account of quantum geometry from a statistical field theory point of view. The approach uses discrete approximations and develops analytical and numerical tools. Continuum physics is recovered through scaling limits at phase transition points and the relation to conformal quantum field theories coupled to quantum gravity is described. The most important numerical work is covered, but the main aim is to develop mathematically precise results that have wide applications. Many diagrams and references are included.