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Non-Critical String Theory: Classical and Quantum Aspects
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Authors: Stanislav Klimenko and Igor Nikitin (Institute of Computing for Physics and Technology, Protvino, Russia) 
Book Description:
The relativistic string theory was born in 1960s. The stimulus was an observation that the dual model of hadronic interactions proposed by Veneziano is adequate not to the quantum theory of usual (null-dimensional) particles but to the theory of one-dimensional relativistic objects - the strings. It has been immediately found that a self-consistent quantum theory of (bosonic) relativistic strings can be constructed in frames of standard quantization scheme only in a space-time of dimension 26. Inclusion of fermions has decreased this critical dimension to 10. However, it is evident from the experiment, that elementary particles and their constituents ``live'' in the space-time of dimension 4. The attempt to show that extra 6 dimensions are compactified on the scale of Planck's length, in the spirit of old ideas by Kaluza-Klein, just created further complications.
This book differs from traditional presentations of the classical and quantum theory of relativistic strings by two aspects. First, it proposes and consistently implements an idea of mathematical modeling and computer visualization of topologically non-trivial solutions of the classical equations of motion of relativistic strings. Second, on this basis it successfully implements a quantization scheme, originating from the papers by G.P.Pron'ko, which uses a different set of dynamical variables, canonically equivalent to the variables of standard scheme, in frames of Hamiltonian formalism and Dirac's quantization procedure.

Table of Contents:
Preface

Introduction

Color plates

Chapter 1 - Structure of classical solutions of Nambu-Goto model; pp. 1-81
1.1 MathematicalbackgroundoftheclassicalNambu-Gotomodel
1.2 Classificationofsingularitiesonworldsheets
1.3 Classofexoticsolutions
1.4 Classofsolutionswithbreaks
1.5 Gribov’scopiesinsolutionsspace
1.6 Supplement:proofoflemmas

Chapter 2 - Structure of quantum solutions of Nambu-Goto model;
pp. 83-144
2.1 MathematicalbackgroundofthequantumNambu-Gotomodel
2.2 Dirac’squantizationofspecialcases
2.3 Gupta-Bleuler’squantizationofthegeneralcase
2.4 Dirac’squantizationofthegeneralcase
2.5 Supplement:proofoflemmas30-42

Chapter 3 - Computational methods and algorithms used in the investigation of Nambu-Goto model; pp. 145-179
3.1 Computervisualizationofstringdynamics
3.2 Gro¨bnerbasesforinvestigationofpolynomialsystems
3.3 Factorizationofmatrixpolynomials
3.4 Algorithmsofmatrixcompression
3.5 Generationofquantumspectra

Bibliography
List of denotations
Subject index

   Binding: Hardcover
   Pub. Date: 2007
   ISBN: 1-59454-267-8
   Status: AV
  
Status Code Description
AN Announcing
FM Formatting
PP Page Proofs
FP Final Production
EP Editorial Production
PR At Prepress
AP At Press
AV Available
  
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Non-Critical String Theory: Classical and Quantum Aspects