Note: Front Cover -- Lattice 91 -- Copyright Page -- PREFACE -- Table of Contents -- Part 1: Plenary Talks -- Section 1.1: Reviews -- CHAPTER 1. THE QCD SPECTRUM AND PHASE DIAGRAM ON THE LATTICE - 1991 -- Introduction -- The QCD spectrum on the lattice -- Phase structure of QCD -- Acknowledgments -- References -- CHAPTER 2. QCD AT FINITE DENSITY -- 1. Formulation -- 2. The Quenched Approximation [3] -- 3. Monte-Carlo simulations with dynamical fermions -- 4. The Propagator Matrix -- 5. Monte-Carlo simulations measuring the canonical partition functions in SU (3) -- Acknowledgements -- References -- CHAPTER 3. WEAK MATRIX ELEMENTS -- Introduction -- The kaon B-parameter -- Divergent Operators -- Conclusion -- Acknowledgements -- References -- CHAPTER 4. SIMULATING HEAVY QUARKS -- 1. Introduction -- 2. Why Study Quarkonium? -- 3. Dirac Quarks-Wilson's Action -- 4. Nonrelativistic Quarks-NRQCD -- 5. Static Quarks -- 6. Lattice Perturbation Theory -- 7. Applications -- 8. Summary and Conclusions -- Acknowledgements -- References -- CHAPTER 5. HIGGS- AND YUKAWA-THEORIES ON THE LATTICE -- 1. INTRODUCTION -- 2. SCALAR HIGGS MODELS -- 3. SCALAR-FERMION YUKAWA-MODELS -- 4. SUMMARY AND CONCLUSIONS -- References -- CHAPTER 6. SPHALERON INDUCED BARYON NUMBER NON-CONSERVATION -- 1. Introduction -- 2. Rate of sphaleron transitions at high temperatures -- 3. Real time lattice simulations of sphaleron transitions -- 4. Electroweak baryogenesis -- 5. Conclusion -- References -- CHAPTER 7. QUANTUM GRAVITY AND RANDOM SURFACES -- 1. Introduction -- 2. Two-dimensional quantum gravity -- 3. Random surfaces -- 4. Quantum gravity in d > -- 2 -- 5. Conclusion -- Acknowledgements -- References -- CHAPTER 8. RECENT ANALYTIC PROGRESS ON FINITE SIZE EFFECTS -- 1. INTRODUCTION -- 2. SIGNATURES OF RESONANCES IN FINITE VOLUME -- 3. CHIRAL PERTURBATION THEORY. , 4. THE THERMODYNAMIC BETHE ANSATZ -- 5. DETERMINATION OF THE RUNNING COUPLING -- 6. FIRST ORDER TRANSITIONS -- References -- CHAPTER 9. PARALLEL QCD MACHINES -- 1. INTRODUCTION -- 2. BACKGROUND -- 3. FIRST GENERATION -- 4. SECOND GENERATION -- 5. COMMERCIAL MACHINES -- 6. NEW PROJECTS -- 7. CONCLUSIONS -- References -- CHAPTER 10. MULTIGRID METHODS IN LATTICE FIELD COMPUTATIONS -- 1. Elementary Acquaintance with Multigrid -- 2. Introduction -- 3. Multigrid PDE Solvers -- 4. Multigrid Dirac Solver -- 5. Multiscale Statistical Simulations -- 6. Other Relevant Multilevel Techniques -- Acknowledgements -- References -- CHAPTER 11. THEORY AND NUMERICAL SIMULATION OF COMPUTATIONALLY DIFFICULT SYSTEMS -- 1. Introduction -- 2. NP Completeness -- 3. The Energy Landscape -- 4. The Pure States -- 5. Some Soluble Models -- 6. An Open Case: Three Dimensional Spin Glasses -- 7. Pinned Manifolds -- 8. Random Self-Interacting Heteropolymers -- 9. Conclusions -- References -- Section 1.2: Topical Talks -- CHAPTER 12. TOWARDS THE CONTINUUM LIMIT OF STAGGERED WEAK MATRIX ELEMENTS -- 1. INTRODUCTION -- 2. FLAVOR SYMMETRY BREAKING -- 3. SCALING OF QUENCHED BK -- 4. IMPROVED OPERATORS -- ACKNOWLEDGEMENTS -- References -- CHAPTER 13. LATTICE APPROACH TO SEMI-LEPTONIC DECAYS OF CHARM MESONS -- 1. Introduction -- 2. The Status at LAT'90 -- 3. Experiments and Phenomenology -- 4. Lattice Methodology and Differences in Implementation -- 5. Results -- 6. Remarks on the Pole-Dominance Model and on the End-point Region -- 7. Conclusions and Summary -- Acknowledgements -- References -- CHAPTER 14. FIRST RESULTS FROM THE UKQCD COLLABORATION -- 1. Introduction -- 2. Details of Simulation -- 3. Static Q - Q Potentials -- 4. The Hadron Spectrum -- Conclusions -- References -- CHAPTER 15. RECENT RESULTS FROM THE 256-NODE COLUMBIA MACHINE -- 1. Introduction -- 2. Nt = 2 Hadron Masses. , References -- CHAPTER 16. INVESTIGATION OF THE FERMION SPECTRUM AT STRONG WILSON-YUKAWA COUPLING IN THE SYMMETRIC PHASE -- 1. INTRODUCTION -- 2. THE FERMION SPECTRUM IN THE PMS PHASE -- 3. THE NEUTRAL FERMION SECTOR -- 4. THE CHARGED FERMION SECTOR -- 5. FINAL REMARKS -- References -- CHAPTER 17. ON LATTICE CHIRAL GAUGE THEORIES -- References -- CHAPTER 18. THE GENERALIZED NAMBU-JONA-LASINIO MECHANISM AND THE STANDARD MODEL -- 1. Introduction -- 2. The Nambu-Jona-Lasinio Model -- 3. Equivalent Higgs-Yukawa Model -- 4. Equivalence Proof in the 1/N Expansion -- 5. Hill's Toy Model and the NJL Condensate -- 6. Conclusions -- Acknowledgements -- References -- CHAPTER 19. VORTEX SCATTERING IN THE ABELIAN HIGGS MODEL -- References -- CHAPTER 20. THE EXACT MASS GAP IN D=2 ASYMPTOTICALLY FREE FIELD THEORIES AND RELATED EXPERIMENTAL RESULTS -- 1. Introduction and Summary -- 2. An Application: The Magnetic Correlation Length of La2CuO4 Compounds at Low Temperatures -- 3. General Steps and Assumptions Leading to the Mass Gap Predictions -- Acknowledgements -- References -- CHAPTER 21. ON SELF ORGANIZED CRITICALITY -- Acknowledgement -- References -- Part 2: Parallel Sessions -- Section 2.1 QCD -- 2.1.1 QCD Spectroscopy -- CHAPTER 22. QCD HADRON SPECTROSCOPY WITH STAGGERED DYNAMICAL QUARKS AT -- Acknowledgements -- References -- CHAPTER 23. FINITE-SIZE EFFECTS AND Tc FOR ß = 5.445 WITH TWO STAGGERED FLAVORS -- References -- CHAPTER 24. FULL QCD HADRON SPECTROSCOPY AT ß = 5.7 -- 1. INTRODUCTION -- 2. FINITE-SIZE EFFECT -- 3. PHYSICAL SCALE OF THE LATTICE -- 4. fπ AND BK IN FULL QCD -- References -- CHAPTER 25. HADRON SPECTRUM AND INTERQUARK FORCES: RESULTS FROM THE MTC COLLABORATION -- 1. HADRON SPECTRUM -- 2. CHIRAL SECTOR -- 3. HEAVY QUARK POTENTIAL -- References -- CHAPTER 26. SIMULATIONS OF 2-FLAVOR QCD ON A 324 LATTICE AT ß = 5.7 -- 1. INTRODUCTION. , 2. Tests of 163 x 32 Simulation -- 3. Currently running 324 simulations -- References -- CHAPTER 27. DYNAMICAL QUARK EFFECTS ON GLUEBALLS AND TOPOLOGY IN LATTICE QCD -- 1. INTRODUCTION -- 2. GLUEBALL MASS SPECTRUM -- 3. TOPOLOGICAL SUSCEPTIBILITY -- References -- CHAPTER 28. THE QUENCHED MASS SPECTRUM IN LATTICE QCD -- 1. Introduction -- 2. The Hadron Masses and the Chiral Limit -- 3. The Mass Splittings -- 4. The Physical Mass Values and the Scaling Behaviour -- 5. Decay Constants and the Nucleon σ Term -- References -- CHAPTER 29. QUENCHED HADRON SPECTRUM ON A 243 x 54 LATTICE -- References -- CHAPTER 30. FLAVOR SYMMETRY OF HADRON MASSES WITH STAGGERED FERMIONS -- 1. Introduction -- 2. Wall Source Technique -- 3. Result -- 4. Summary -- References -- CHAPTER 31. VOLUME DEPENDENCE OF THE VALENCE WILSON FERMION MASS SPECTRUM -- References -- CHAPTER 32. QCD SPECTROSCOPY AND PHENOMENOLOGY WITH IMPROVED ACTIONS -- 1. Introduction -- 2. Phenomenology: Clover vs. Wilson -- 3. Spectroscopy with the Hamber-Wu Action -- References -- CHAPTER 33. HADRON SPECTROSCOPY ON A 323 x 48 LATTICE -- 1. Introduction -- 2. Measurement of Hadron Propagators -- Acknowledgment -- References -- 2.1.2 Finite-Temperature QCD -- CHAPTER 34. THE CHIRAL PHASE TRANSITION IN QCD: CRITICAL EXPONENTS AND THEIR FLAVOUR DEPENDENCE -- 1. UNIVERSALITY AND CHIRAL SYMMETRY ON THE LATTICE -- 2. ONE SPECIES OF STAGGERED FERMIONS -- 3. SEVERAL SPECIES OF STAGGERED FERMIONS -- References -- CHAPTER 35. DECONFINING TRANSITION OF SU(S) GAUGE THEORY ON NT = 6 LATTICES -- References -- CHAPTER 36. QCD THERMODYNAMICS WITH TWO FLAVORS OF QUARKS[1] -- References -- CHAPTER 37. THERMODYNAMICS OF LATTICE QCD WITH 2 LIGHT DYNAMICAL (STAGGERED) QUARK FLAVOURS ON A 163 x 8 LATTICE -- References -- CHAPTER 38. QUARK CONFINEMENT AND NUMBER OF FLAVORS -- References. , CHAPTER 39. QCD PHASE STRUCTURE WITH 8 LIGHT QUARK FLAVORS -- 1. Introduction -- 2. Strong First Order Transition and ßc -- 4. Chiral Properties of the Phases -- 5. Conclusion -- References -- CHAPTER 40. THE BUBBLE FREE ENERGY IN THE QCD PHASE TRANSITION -- References -- CHAPTER 41. FULL QCD AND QED AT FINITE TEMPERATURE AND CHEMICAL POTENTIAL -- 1. Full QCD on anisotropic lattices -- 2. Full QED with finite chemical potential -- References -- CHAPTER 42. SCREENING IN HOT QCD -- ACKNOWLEDGEMENTS -- References -- CHAPTER 43. COMPLEX ZEROS OF THE PARTITION FUNCTION FOR LATTICE GAUGE THEORIES -- 1. Introduction -- 2. Z[m,ß] as a Polynomial in the Mass -- 3. Results -- References -- CHAPTER 44. THE DEBYE SCREENING IN THE QUARK-GLUON PLASMA -- References -- 2.1.3 Weak Matrix Elements -- CHAPTER 45. MATRIX ELEMENTS WITH WILSON FERMIONS -- 1. INTRODUCTION -- 2. SURPRISES IN HADRON SPECTRUM -- 3. MESON DECAY CONSTANTS -- 4. CHIRAL PARAMETERS mq and ψψ -- 5. KAON B PARAMETER -- ACKNOWLEDGEMENTS -- References -- CHAPTER 46. IMPROVED LATTICE QCD -- 1. Introduction -- 2. Next-to-nearest-neighbor improved action -- 3. Nearest-neighbor improved action -- Acknowledgements -- References -- CHAPTER 47. HEAVY FLAVOR MESON DECAY CONSTANTS WITH WILSON FERMIONS AT ß = 6.4 -- References -- CHAPTER 48. FLAVOR CHANGING NEUTRAL CURRENT TRANSITIONS ON THE LATTICE FOR HEAVY-LIGHT SYSTEMS -- References -- CHAPTER 49. SCALAR AND AXIAL MATRIX ELEMENTS OF THE NUCLEON: SEA QUARK CONTENT -- ACKNOWLEDGEMENTS -- References -- CHAPTER 50. QUARK LOOP CALCULATIONS -- References -- CHAPTER 51. THE QUARK FRACTION OF THE PROTON SPIN -- 1. INTRODUCTION -- 2. THEORETICAL PRELIMINARIES -- 3. LATTICE ANALYSIS -- 4. RESULTS -- 5. CONCLUSIONS -- ACKNOWLEDGEMENTS -- References -- CHAPTER 52. CHIRAL PERTURBATION THEORY FOR THE QUENCHED APPROXIMATION -- References. , CHAPTER 53. FROM THE LATTICE WORLD TO THE REAL WORLD.