Overview

This volume contains a series of lectures written for researchers and graduate students, which includes many strongly debated aspects of quantum field theory including anomalies, chiral-symmetry breaking, phase transitions, integrable models and quantum groups. The book concludes with a status report on the high-energy accelerator LEP and its implications for the standard electroweak model.

Full Product Details

Author:   Heinrich Mitter ,  Wolfgang Schweiger
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Weight:   0.630kg
ISBN:  

9783540531784

ISBN 10:   3540531785
Pages:   296
Publication Date:   08 January 1991
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   Out of stock  

Table of Contents

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.

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