Geometric Phases in Physics
During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a paper by Michael Berry, where it was found that the adiabatic evolution of energy eigenfunctions in quantum mechanics contains a phase of geometric origin (now known as ‘Berry's phase’) in addition to the usual dynamical phase derived from Schrödinger's equation. This observation, though basically elementary, seems to be quite profound. Phases with similar mathematical origins have been identified and found to be important in a startling variety of physical contexts, ranging from nuclear magnetic resonance and low-Reynolds number hydrodynamics to quantum field theory. This volume is a collection of original papers and reprints, with commentary, on the subject.
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INTRODUCTION AND OVERVIEW
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adiabatic phase adiabatic theorem Aharonov amplitude angular momentum anomaly axis beam Berry's phase Born-Oppenheimer bosons bundle calculation Chem circuit classical closed path configuration space conical intersections connection consider coordinates corresponding curve cyclic defined deformations degeneracy depends derivative Dirac discussed eigenfunctions eigenstates eigenvalues electronic energy evolution example fermions fiber flux formula fractional statistics gauge field gauge potential gauge transformation geometrical phase given Hamiltonian holonomy infinitesimal interaction Jackiw Lett loop low Reynolds number M. V. Berry magnetic field magnetic monopole matrix Mead molecular molecule motion non-Abelian nuclear obtained Pancharatnam parallel transport parameter space particle path integral phase change phase factor PHYSICAL REVIEW LETTERS plane polarisation polarization problem Proc quantization quantum mechanics quantum numbers result rotation Schrodinger equation shape skyrmion solid angle solitons solution sphere spin surface symmetry term tion topological Truhlar vanish variables vector potential vibration wave function wavefunction Wilczek zero