Quantum Adiabatic Phases And Chiral Gauge Anomalies
The quantum adiabatic phase [1,2] has recently emerged as a universal element in the topological analysis of various quantum mechanical problems. It can be understood as an Ahoronov-Bohm effect on the parameter space of a quantum mechanical system and has seen numerous applications, notably to the analysis of corrections to semiclassical quantization [2,3,4], the statistics of quasiparticles such as vortices in two dimensional systems [6,6,7], adiabatic effective actions, the quantum Hall effect  and chiral anomalies in the Hamiltonian, Schrödinger picture of gauge theories . Furthermore, some of its predicted interference phenomena have recently found good agreement with experiment [10,11]. In this review we shall give a simple account of the origin of the quantum adiabatic phase, describe how the concept is used to construct adiabatic effective actions and discuss chiral gauge anomalies within this framework.
KeywordsVortex Manifold Schiff Haldane
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