Physics and mathematics of strings / editors, L. Brink, D. Friedan, A.M. Polyakov.

Format:

Book

Contributor:

Brink, Lars.

Friedan, D.

Knizhnik, Vadim, 1962-1987.

Polyakov, A. M.

Language:

English

Subjects (All):

Mathematical physics.

Physics.

Physical Description:

1 online resource (609 p.)

Place of Publication:

Singapore ; Teaneck, NJ : World Scientific, c1990.

Language Note:

English

Summary:

Vadim Knizhnik was one of the most promising theoretical physicists in the world. Unfortunately, he passed away at the very young age of 25 years. This memorial volume is to honor his contributions in Theoretical Physics. This is perhaps one of the most important collections of articles on the theoretical developments in String Theory, Conformal Field Theory and related topics. It consists of contributions from world-renowned physicists who have met Vadim Knizhnik personally and whom the late Knizhnik really respected. The contributions are systematic and pedagogical in format.

Contents:

FOREWORD; CONTENTS; GAUGE TRANSFORMATIONS AND DIFFEOMORPHISMS; I. INTRODUCTION; II. DIFFEOMORPHISMS OUT OF GAUGE TRANSFORMATIONS; III. CONSEQUENCES FOR WZNW ACTIONS; IV. THE CASE OF SL(3); ACKNOWLEDGEMENTS; REFERENCES; TOPICS IN CONFORMAL FIELD THEORY; 1. Introduction; 2. General Properties of a Conformal Field Theory; 2.1 Conformal Invariance and Conformal Ward Identities; 2.2 Conformal blocks and duality; 3. Degenerate Conformal Families. Coulomb Gas Repretation; 3.1 Generalities; 3.2 Coulomb gas representation. Fusion rules; 3.3 Virasoro characters and null vectors

3.4 Sample computations: conformal blocks and braiding matrices4. Current Algebras and Wess-Zumino-Witten Models; 4.1 Generalities; 4.2 Representations and fusion rules; 4.3 Partition functions, modular invariants; 5. Fusion Algebras. The Verlinde Conjecture; 5.1 The fusion algebra and its properties; 5.2 Proof of the Verlinde conjecture; 5.3 Constraints from rationality; 6 Duality and Quantum Groups; 6.1 Motivation; 6.2 Quantum groups and their representations for q a root of unity; 7. Explicit Examples and Modular Properties; 7.1 WZW models; 7.2 Rational gaussian modelt

7.3 Modular properties8. Solvable Lattice Models and Conformal Field Theories; 8.1 Vertex models; 8.1.1 Regular lattice; 8.1.2 Nonregular lattice. Z-invariance; 8.2 RSOS-models65; 8.3 Conformal field theory; 9. Knots Conformal Field Theories and Statistical Mechanics; 9.1 Knot theory; 9.2 State models: Turaev and Kauffman invariants; 9.3 Rational conformal field theories and knots invariants; 9.4 Knots on arbitrary 3- manifolds; References; Representations of Uq (gl(n,C)) at q = 0 and the Robinson-Shensted correspondence; 1. Introduction; 2. Representation of Uq(g1(n,C)) at q = 0.

2.1. Uq{BKn,C)).2.2. Gelfand- Tsetlin pattern.; 2.3. Irreducible representations of Uq(g1(n,C)).; 2.4. Wigner coefficients.; 2.5. Paths.; 2.6. Limit of the Wigner coefficients.; 2.7. Insertion-deletion.; 2.8. Interpretation of the q±1® 0 iimit by semi-standard tableaux.; 2.9. Standard tableaux and irreducible decomposition of VÄN.; 2.10. The Robinson-Shensted correspondence.; 2.11. Decomposition ofV®N at q±1 = 0.; 3. R-matrix in the scaling region; 3.1. R-matrix for symmetric tensor representations.; 3.2. Characterization of the space V(P).; 3.3. Spectral decomposition: The case of Vy ® Vm.

References.THE SEWING TECHNIQUE AND CORRELATION FUNCTIONS ON ARBITRARY RIEMANN SURFACES; 1 Introduction; 2 Free Bosonic Theory; 3 Free Fermionic Theory; 4 Bosonization Rules; References; SUPERGRASSMANNIANS, SUPER r-FUNCTIONS AND STRINGS; References; CONFORMAL FIELD THEORY AND PURELY ELASTIC S-MATRICES; 1. Introduction; 2. Integrals of Motion in the Models H3, H4, H6; 3, Purely Elastic S-Matrices and Integrals of Motion; 4. Scaling Limit of the T = TC Ising Model with Magnetic Field; 5. Thermal Shift Away From the Ising Tricritical Point

6. Thermal Deformation of the Tricritical 3-State Potts Model

Notes:

"Memorial volume for Vadim Knizhnik."

Includes bibliographical references.

ISBN:

9781299280861

1299280862

9789814434461

9814434469

OCLC:

830161967