Quantum Mechanics of Fundamental Systems 2

1 Anomalous Jacobians and the Vector Anomaly.- 1. Introduction.- 2. The Schwinger Model.- 3. The Method of Fujikawa.- 4. Redefinition of the Jacobian.- 5. Regulated Phase Transformations.- 6. Conclusions and Open Problems.- References.- 2 String Phenomenology.- 1. Introduction.- 2. Gauge Symmetries and Global Symmetries.- 3. Space-Time Supersymmetry in String Theory.- 4. Conclusions.- References.- 3 Open Gauge Algebra and Ghost Unification.- 4 Algebras of the Virasoro, Neveu-Schwarz, and Ramond Types on Genus g Riemann Surfaces.- 1. Introduction.- 2. The Bases.- 3. The Central Extensions.- 4. A String Realization.- 5. Quantization.- 6. The BRST Operator.- References.- 5 Quantum Groups, Integrable Theories, and Conformed Models.- 6 Small Handles and Auxiliary Fields.- 7 Differential Equations in Moduli Space.- 8 Consistent Quantum Mechanics of Chiral p-Forms.- 1. Introduction.- 2. Chiral Bosons-Classical Analysis.- 3. Chiral Bosons-Quantum Theory.- 4. Chiral p-Forms.- References.- 9 First and Second Quantized Point Particles of Any Spin.- 1. Introduction.- 2. More on the Extensions of the Mass Shell Algebra.- 3. Explicit Realizations.- 4. Light-Cone Gauge Quantization.- 5. Dirac Quantization.- 6. BRST Quantization.- 7. Second Quantized Theory.- References.- 10 Strings in Space.- 11 Covariantized Light-Cone String Field Theory.- 1. Motivation.- 2. Covariantized Light-Cone SFTs: Introduction.- 3. Light-Cone Gauge String Field Theory.- 4. From Light-Cone to Covariant SFT: General Procedure.- 5. Gauge-Fixed BRS-Invariant Action and Physical States.- 6. Another Gauge-Fixed Action: Siegel's Original One.- Appendix A: Solutions to Equation (55a).- Appendix B: Proof of the Generalized Parisi-Sourlas Formula (68).- References.- 12 Topology, Superspace, and Anomalies.- 13 Field and String Quantization in Curved Space-Times.- 1. Contextual Background.- 2. Fields in Curved Space.- 3. Strings in Rindler Space.- 4. Horizon Regularization in Rindler Space-Introduction of the s Parameter.- 5. Analytic Mappings and the Hawking-Unruh Effect in String Theory.- 6. Transformation between the States. Derivation of the Parameter ? from the Constraint Equations.- 7. Strings near Black Holes.- 8. New Approach to String Quantization in Curved Space Times 226 References.- 14 Symmetries and Anomalies in Fermionic Theories.- 1. Introduction.- 2. Quantization of Gauge Theories with Weyl Fermions (Or: Are Anomalies Anomalous?).- 3. Conformal Invariance of the Chiral Gross-Neveu Model.- References.- 15 Differential Algebras in Field Theory.- 1. Introduction.- 2. Yang-Mills Theories and First Quantized Strings.- 3. The Algebraic Structure of Local Anomalies.- 4. Lessons to Be Drawn.- References.- 16 Supermembrances, Superstrings, and Supergravity.- 1. Introduction.- 2. Nonlinearity. Absence of Weyl Invariance, and Nonrenormalizability.- 3. Classical GS Superstrings and Classical GS Supermembrances.- 4. Local ? Symmetry.- 5. Rigid World-Sheet SUSY.- References.- 17 Thirring Strings: Use of Generalized Nonabelian Bosonization Techniques.- 1. Introduction: Conformal Invariant String Theories in a Compactified Space.- 2. Bosonization and Fermionization in Conformally Invariant Two-Dimensional Field Theories.- 3. The Thirring Model and Strings.- 4. Vertices and String Theory.- 5. Conclusions.- References.