The role of topology in classical and quantum physics

Lecture Notes in Physics: Monographs 7 ......Page 2
The role of topology in classical and quantum physics ......Page 4
Preface ......Page 6
CONTENTS ......Page 11
1.1. Introduction ......Page 14
1.2. Some examples ......Page 15
1.3. Topology of Defects (the case of planar spins) ......Page 17
1.4. The Fundamental Group ......Page 21
1.5. The Abstract Fundamental Group. Conjugacy Classes and Freely Homotopic Loops ......Page 31
1.6. The Order-Parameter Space as a Ccset Space ......Page 41
1.7. Preliminary Theorems Concerning Fundamental Groups ......Page 55
1.8. Higher Homotopy Groups ......Page 59
1.9. Relative Homotopy and Relative Homotopy Groups ......Page 70
1.10. The Exact Homotopy Sequence ......Page 71
2.1. Introduction ......Page 80
2.2. The Pontrjagin Index and the Hopf Invariant ......Page 87
2.3. The SO(3) Nonlinear Sigma-Models in One and Two Space Dimensions ......Page 98
2.4. The d=2 SO(3) Nonlinear Sigma-Model as a Gauge Theory ......Page 108
2.5. The Ginnsburg-Landan Theory of Superconductivity ......Page 117
3.1. Introduction ......Page 127
3.2. Quantnm Mechanics in Nonsimply-connected Spaces ......Page 130
3.3. The Case of Identical Particles ......Page 137
3.4. Dynamical Implementation of Braid Statistics ......Page 148
4.1. Introduction ......Page 158
4.2. Chern-Simons Lagrangians ......Page 159
4.3. Charged Particles Interacting with a CS Field ......Page 166
4.4. Gauge Fixing and an Explicit Solution for A_mu ......Page 172
4.5. Effective Lagrangian for (Statistical) Particle Interaction ......Page 180
5.1. Introduction ......Page 185
5.2. Light Polarization, the Hopf Bundle and Pancharatnam's Phase ......Page 186
5.3. The Quantum Adiabatic Phase ......Page 194
6.1. Introduction ......Page 204
6.2. Preliminaries ......Page 207
6.3. The Classical Hall Effect ......Page 214
6.4. Bloch Electrons in a Magnetic Field ......Page 216
6.5. The Integer Quantum Hall Effect ......Page 223
6.6. The Fractional Quantum Hall Effect ......Page 230
6.7. Fractionally-Charged Quasiparticles and the Hierarchy of Quantum Hall States ......Page 235
REFERENCES ......Page 244