The Role of Topology in Classical and Quantum Physics, Volume 7In solid-state physics especially topological techniques have turned out to be extremely useful for modelling and explaining physical properties of matter. This book illustrates various applications of algebraic topology in classical field theory (non-linear sigma-models) and in quantizationsin multiply connected spaces (anyons). It treats Chern-Simon Lagrangians, Berry's phase, the polarization of light and the fractional quantum Hall effect. |
Contents
AN ELEMENTARY INTRODUCTION TO ALGEBRAIC | 1 |
TOPOLOGICAL METHODS IN CLASSICAL FIELD | 67 |
INEQUIVALENT QUANTIZATIONS IN MULTIPLY | 114 |
TOPICS IN CHERNSIMONS PHYSICS | 145 |
A SHORT INTRODUCTION TO CONNECTIONS | 172 |
ELECTRONS IN A MAGNETIC FIELD AND A CURSORY | 191 |
REFERENCES | 231 |
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Common terms and phrases
abelian action actually adiabatic already angle associated assume becomes boundary bundle called charge classical closed complex condition conductivity connected consider construction coordinates corresponding covering defects defined definition density depend derivatives described Differential direction discussed effect electrons element elementary equations example factor field flux fractional gauge given Hall Hamiltonian hence homotopy homotopy class homotopy group Hopf identity implies integer interaction introduce invariant Lagrangian latter leads loop magnetic field manifold namely normal Note obtain operator order parameter original parallel particles path phase Phys Physics plane potential Proceedings projection proof prove quantization Quantum Mechanics reference Remark require result Sect solution space sphere square statistics structure subgroup term Theorem theory topological turn unit vector wave function wavefunction winding number