This volume is based on a meeting on Quantum Mechanics of Fundamental Systems, held December 17-20 of 1987, at the Centro de Estudios Cientificos de Santiago (CECS). The meeting was intended to review new developments in the field defined by its purposely vague title. We were especially interested in communicating important advances in a broad perspective and in a self-contained manner to a wide colleague ship, and in particular to Latin American physicists. Whatever success we may have achieved in that direction would cer tainly not have been possible without the help and generosity of many people. For their kind support we thank the Tinker Foundation, the Inter national Centre for Theoretical Physics, the Ministere des Affaires Etrangeres et Service Culturel et de Cooperation Scientifique et Technique de France and the Centro Latinoamericano de Fisica. We are especially grateful to the Santiago College and to its principal, Rebeca Donoso, for allowing us to hold the meeting at that school when, at the last moment, we were deprived of the previously arranged meeting site. Last but not least we thank the participants for an extraordinary week and the CECS staff for performing, as usual, beyond any reasonable expectation.

Zusammenfassung
Studies based on a meeting held at the Centro de Estudios Cientificos de Santiago, Dec. 17-20, 1987, review new developments in the field. Areas covered include: anomalous Jacobians and the vector anomaly; string phenomenology; quantum groups, integrable theories, and conformed models, small handles

Inhalt
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 BosonsClassical Analysis.- 3. Chiral BosonsQuantum 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 SpaceIntroduction 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.