Random Surfaces and Quantum Gravity

Random Surfaces and Quantum Gravity
Title Random Surfaces and Quantum Gravity PDF eBook
Author Orlando Alvarez
Publisher Springer Science & Business Media
Total Pages 401
Release 2013-03-09
Genre Science
ISBN 146153772X

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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

Two Dimensional Quantum Gravity And Random Surfaces - 8th Jerusalem Winter School For Theoretical Physics

Two Dimensional Quantum Gravity And Random Surfaces - 8th Jerusalem Winter School For Theoretical Physics
Title Two Dimensional Quantum Gravity And Random Surfaces - 8th Jerusalem Winter School For Theoretical Physics PDF eBook
Author David J Gross
Publisher World Scientific
Total Pages 256
Release 1991-12-17
Genre
ISBN 9814556300

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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.

Two Dimensional Quantum Gravity and Random Surfaces

Two Dimensional Quantum Gravity and Random Surfaces
Title Two Dimensional Quantum Gravity and Random Surfaces PDF eBook
Author David Gross
Publisher
Total Pages 240
Release 1992
Genre SCIENCE
ISBN 9789814538992

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Two Dimensional Quantum Gravity and Random Surfaces

Two Dimensional Quantum Gravity and Random Surfaces
Title Two Dimensional Quantum Gravity and Random Surfaces PDF eBook
Author David J. Gross
Publisher
Total Pages 240
Release 1992
Genre
ISBN 9789810206437

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Random Surfaces

Random Surfaces
Title Random Surfaces PDF eBook
Author Scott Sheffield
Publisher
Total Pages 194
Release 2005
Genre Gibbs' free energy
ISBN

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Random Surfaces and 2D Quantum Gravity

Random Surfaces and 2D Quantum Gravity
Title Random Surfaces and 2D Quantum Gravity PDF eBook
Author Jan Ambjørn
Publisher
Total Pages 217
Release 1992
Genre Quantum gravity
ISBN

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Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory

Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory
Title Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory PDF eBook
Author Roberto Fernandez
Publisher Springer Science & Business Media
Total Pages 446
Release 2013-03-14
Genre Science
ISBN 3662028662

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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.