608 pages, 10x7 inches
July 2002 Hardcover
ISBN 1-58949-021-5


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Recent years have witnessed increasing interests in physics in noncommutative space, and noncommutative space-time. The notion of quantized space-time and that of noncommuting guiding-center coordinates in the lowest Landau level have existed for quite a while. Lately since the discovery of noncommutative field theories in matrix models that describe string theory nonperturbatively, noncommutative Yang-Mills and its cousins have been explored extensively in hundreds of papers in the literature. One expects that a large part of efforts in string theory will continue to be directed in this direction. Also, many common physical features have been found in string theoretical systems and quantum Hall systems in condensed matter. The goal of this reprint collection is to serve young students and interested researchers with readily available sources of original ideas and useful techniques, and to help to promote communications among different disciplines. The book includes eight chapters, each starting with a brief introduction.

graduate students, professors, and researchers in theoretical physics, mathematical physics and theoretical high energy physics and condensed matter theory. 


0. Foreword

1. Early Papers
     H.S. Snyder: Quantized Space-time
     C.N. Yang: On Quantized Space-time
     J.E. Moyal: Quantum Mechanics as a Statistical Theory

2. A Quick Math Guide
     A. Connes: C* Algebra and Differential Geometry
     A. Connes and M.A. Rieffel: Yang-Mills for Noncommutative Two-tori 
     J. Wess and B. Zumino: Covariant Differential Calculus on the Quantum Hyperplane

     J. Madore: The Fuzzy Sphere

3. Noncommutative Geometry and Quantum Hall Systems
     S.M. Girvin and T. Jach: Formalism for the Quantum Hall Effect: Hilbert Space of Analytic Functions
     V. Pasquier and F.D.M. Haldane: A Dipole Interpretation of the nu =1/2 State
     N. Read
: Lowest-Landau-level Theory of the Quantum Hall Effect: the Fermi-liquid-like State

4. Noncommutative Field Theory in Matrix Mode
     M. Li: Strings from IIB Matrices
     A. Connes, M. R. Douglas and A. Schwarz: Noncommutative Geometry and Matrix Theory: Compactification on Tori
     P. M. Ho and Y. S. Wu: Noncommutative Gauge Theories in Matrix Theory
     H. Aoki, N. Ishibashi, S. Iso, H. Kawai, Y. Kitazawa, and T. Tada: Noncommutative Yang-Mills in IIB Matrix Model
     N. Ishibashi, S. Iso, H. Kawai, and Y. Kitazawa: Wilson Loops in Noncommutative Yang Mills
     D. Kabat and W. Taylor: Spherical Membranes in Matrix Theory

5. Noncommutative Geometry from String Theory
     E. Witten: Bound States of Strings and p-Branes
     P. M. Ho and Y. S. Wu: Noncommutative Geometry and D-Branes
     M. R. Douglas and C. Hull: D-branes and the Noncommutative Torus
     C. S. Chu and P. M. Ho: Noncommutative Open String and D-brane
     V. Schomerus: D-branes and Deformation Quantization
    N. Seiberg and E. Witten: String Theory and Noncommutative Geometry

6. Quantum Effects in NCFT
     T. Filk: Divergencies in a Field Theory on Quantum Space
     D. Bigatti and L. Susskind: Magnetic Fields, Branes and Noncommutative Geometry
     S. Minwalla, M. Van Raamsdonk, N. Seiberg: Noncommutative Perturbative Dynamics
     A. Armoni: Comments on Perturbative Dynamics of Non-Commutative Yang-Mills Theory

7. Instantons and Solitons in NCFT
     N. Nekrasov and A. Schwarz: Instantons on Noncommutative R4, and (2,0) Superconformal Six Dimensional Theory
     R. Gopakumar, S. Minwalla, and A. Strominger: Noncommutative Solitons
     J. A. Harvey, P. Kraus, F. Larsen, and E. J. Martinec: D-branes and Strings as Non-commutative Solitons
     D. Gross and N. Nekrasov: Monopoles and Strings in Noncommutative Gauge Theory

8. Gravity Dual of Noncommutative Gauge Theories
     J. M. Maldacena and J. G. Russo: Large N Limit of Non-Commutative Gauge Theories
     M. Li and Y. S. Wu: Holography and Noncommutative Yang-Mills
     S. R. Das and S. J. Rey: Open Wilson Lines in Noncommutative Gauge Theory and Tomography of Holographic Dual Supergravity