Fields and Particles de Heinrich Mitter

Fields and Particles: Proceedings of the XXIX Int. Universitätswochen für Kernphysik, Schladming, Austria, March 1990

Heinrich Mitter

Wolfgang Schweiger

en Limba Engleză Paperback – 21 noi 2011

This volume contains the written versions of invited lectures presented at the 29th "Internationale Universitatswochen fiir Kernphysik" in Schladming, Aus tria, in March 1990. The generous support of our sponsors, the Austrian Ministry of Science and Research, the Government of Styria, and others, made it possible to invite expert lecturers. In choosing the topics of the course we have tried to select some of the currently most fiercely debated aspects of quantum field theory. It is a pleasure for us to thank all the speakers for their excellent presentations and their efforts in preparing the lecture notes. After the school the lecture notes were revised by the authors and partly rewritten ~n '!EX. We are also indebted to Mrs. Neuhold for the careful typing of those notes which we did not receive in '!EX. Graz, Austria H. Mitter July 1990 W. Schweiger Contents An Introduction to Integrable Models and Conformal Field Theory By H. Grosse (With 6 Figures) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1 1. Introduction ............................................. . 1 1.1 Continuous Integrable Models .......................... . 1 1.2 "Solvable" Models of Statistical Physics ................. . 2 1.3 The Yang-Baxter Relation ............................. . 3 1.4 Braids and I(nots .................................... . 3 1.5 Confonnal Field Theory d = 2 ......................... . 3 2. Integrable Continuum Models - The Inverse Scattering Method - Solitons .................... . 4 2.1 A General Scheme for Solving (Linear) Problems ......... . 4 2.2 The Direct Step ...................................... . 6 2.3 The Inverse Step ..................................... .

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An Introduction to Integrable Models and Conformal Field Theory.- 1. Introduction.- 1.1 Continuous Integrable Models.- 1.2 “Solvable” Models of Statistical Physics.- 1.3 The Yang-Baxter Relation.- 1.4 Braids and Knots.- 1.5 Conformal Field Theory d = 2.- 2. Integrable Continuum Models — The Inverse Scattering Method — Solitons.- 2.1 A General Scheme for Solving (Linear) Problems.- 2.2 The Direct Step.- 2.3 The Inverse Step.- 2.4 Solutions of the GLM Equation for R ? 0.- 2.5 Solving the KdV Equation.- 2.6 Lax Pairs.- 2.7 Remarks.- 3. Integrable Lattice Systems.- 3.1 Introduction.- 3.2 Ising and Potts Models.- 3.3 The Vertex Model.- 3.4 Connection to Quantum Spin Models.- 3.5 Integrability of the Lattice Model.- 3.6 Bethe States.- 3.7 The Algebraic Bethe Ansatz.- 3.8 Knots, Links and Braids.- 4. Conformal Field Theory.- 4.1 Introduction.- 4.2 Conformal Invariance.- 4.3 Local Conformal Transformations d = 2.- 4.4 Three Implications.- 4.5 The Virasoro Algebra.- 4.6 Correlation Functions.- References.- An Introduction to the Renormalization of Theories with Continuous Symmetries, to the Chiral Models and to Their Anomalies.- 1. The Renormalization of Field Equations.- 2. The Renormalization of Models with Continuous Symmetries.- 3. The Chiral Models and Their Current Algebra.- References.- Quantum Field Theory in Low Dimensional Space Time.- 1. Introduction.- 2. The Algebraic Approach to Quantum Field Theory.- 3. Composition of Sectors.- 4. Statistics.- 5. Left Inverses, Markov Traces and the Possible Braid Group Representations.- 6. The 2-Channel Situation.- 7. Exchange Algebras and R-Matrices.- 8. Rehren’s Derivation of the Verlinde Algebra.- 9. Braid Group Statistics in 3 Dimensions.- 10. Conformal Light Cone Theories.- 11. Soliton Sectors in 2d Minkowski Space.- References.- From Integrable Models to Quantum Groups.- 1. Introduction to the Quantum Inverse Scattering Method.- 1.1 The Higher Spin Chain.- 1.2 Complex Spin.- 1.3 The Spin 1/2 XXZ Model.- 1.4 The Higher Spin XXZ Model.- 1.5 The Complex Spin XXZ Model.- 1.6 The Liouville Limit.- 2. Quantum Groups.- 3. The Liouville Model.- 4. The Wess-Zumino-Novikov-Witten Model.- References.- Topics in Planar Physics.- 1. Overview.- 2. Planar Gauge Theories.- 2.1 Topologically Massive Gauge Theories.- 2.2 Non-Abelian Chern-Simons Gauge Theories.- 2.3 Abelian Chern-Simons Gauge Theory with Sources.- 2.4 Quantum Holonomy.- 2.5 Anomalous Statistics and the Spin of Charged Particles.- 2.6 Point-Particles with Abelian Chern-Simons Gauge Fields.- 2.7 Quantum Dynamics.- 3. Planar Gravity.- 3.1 Introduction.- 3.2 Classical Space-Time.- 3.3 Quantum Dynamics.- 3.4 Topological Elaborations.- References.- Boundary Terms, Long Range Effects, and Chiral Symmetry Breaking.- 1. Introduction.- 2. The Hamiltonian Approach: Coupling to the Boundary and Variables at Infinity.- 3. The Lagrangean and Functional Integral Approach. Boundary Ward Identities.- 4. The Schwinger Model and the ? Angle Problem.- 5. Fermionic Integration, Boundary Conditions, and Chiral Symmetry.- 5. References.- Two-Dimensional Nonlinear Sigma Models: Orthodoxy and Heresy.- 1. Introduction.- 2. Beliefs.- 3. Critique.- 4. Heresy: Strategy for a Proof.- 4.1 The FK Representation.- 4.2 Interlude on Percolation Theory.- 4.3 The H Clusters of the O(N).- Model on the Square Lattice at Large ?.- 4.4 From H to FK Clusters.- 5. Conclusions.- References.- Gauge-Independence of Anomalies.- 1. Introduction.- 2. Gauge-Invariance, Gauge-Dependence, External Symmetry.- 3. Quantization.- 4. Extended BRS-Identity, Internal Anomaiy.- 5. External Symmetries, External Anomalies.- 6. Ghost Number Anomaly for the Bosonic String.- 7. The Symmetry Extended BRS-Technique.- 8. Examples.- 8.1 Chiral Anomaly.- 8.2 Horizontal Symmetry.- 8.3 The Bosonic String.- 8.4 The Lorentz Anomaly in Noncovariant Gauges.- 8.5 Chiral Breaking in SUSY YM Theory (Trivial Case).- 8.6 Superconformal Invariance.- Appendix A: A Toy Model for [s,?a] ? 0.- References.- LEPs The First Hundred Days.- 1. Introduction.- 2. Electroweak Physics Results.- 2.1 Outline of the Programme.- 2.2 The Z Mass.- 2.3 Hadronic Peak Cross-Section and Total Width.- 2.4 Hadronic and Leptonic Partial Widths.- 2.5 Constraints on the t-Quark Mass.- 2.6 The Invisible Width and the Number of Neutrino Families.- 2.7 Forward-Backward Asymmetry of Leptons.- 2.8 Summary.- 3. QCD Results.- 3.1 Analysis of Global Event Variables.- 3.2 Analysis of Single-Particle Inclusive Variables.- 3.3 Is ?s Running?.- 4. Searches and Limits.- 4.1 Heavy Sequential Quarks and Charged Leptons.- 4.2 Heavy Neutral Leptons.- 4.3 The Neutral Higgs Boson.- 4.4 Charged Higgs Bosons.- 4.5 Supersymmetric Particles.- 5. LEP: What Next?.- 5.1 A Short-Term Perspective.- 5.2 Plans for the Future.- References.- QCD and Nuclear Structure.- 1. Introduction.- 2. The Realm of Light Nuclei.- 3. A New Interpretation of Conventional Shell Structure.- 4. Conclusion.- References.