Two Dimensional Quantum Gravity And Random Surfaces - 8th Jerusalem Winter School For Theoretical Physics PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Two Dimensional Quantum Gravity And Random Surfaces - 8th Jerusalem Winter School For Theoretical Physics PDF full book. Access full book title Two Dimensional Quantum Gravity And Random Surfaces - 8th Jerusalem Winter School For Theoretical Physics by David J Gross. Download full books in PDF and EPUB format.
Author: David J Gross
Publisher: World Scientific
ISBN: 9814556300
Category :
Languages : en
Pages : 256
Get Book Here
Book Description
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: David J Gross
Publisher: World Scientific
ISBN: 9814556300
Category :
Languages : en
Pages : 256
Get Book Here
Book Description
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: David Gross
Publisher:
ISBN: 9789814538992
Category : SCIENCE
Languages : en
Pages : 240
Get Book Here
Book Description
Author: David Gross
Publisher: World Scientific Publishing Company Incorporated
ISBN: 9789810206420
Category : Science
Languages : en
Pages : 240
Get Book Here
Book Description
Author: Orlando Alvarez
Publisher: Springer Science & Business Media
ISBN: 146153772X
Category : Science
Languages : en
Pages : 401
Get Book Here
Book Description
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: Jan Ambjorn
Publisher: CRC Press
ISBN: 1000776026
Category : Science
Languages : en
Pages : 329
Get Book Here
Book Description
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: Minjae Park (Scientist in mathematics)
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
"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.
Author: Karyn Maureen Apfeldorf
Publisher:
ISBN:
Category :
Languages : en
Pages : 176
Get Book Here
Book Description
Author: Adrian R. Cooper
Publisher:
ISBN:
Category :
Languages : en
Pages : 274
Get Book Here
Book Description
Author: Steven Carlip
Publisher: Cambridge University Press
ISBN: 9780521545884
Category : Science
Languages : en
Pages : 296
Get Book Here
Book Description
The first comprehensive survey of (2+1)-dimensional quantum gravity - for graduate students and researchers.
Author: M. Fukugita
Publisher: Elsevier
ISBN: 1483278050
Category : Science
Languages : en
Pages : 699
Get Book Here
Book Description
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.
