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Physical Review Letters

Geometric Canonical Phase Factors and Path Integrals

Hiroshi Kuratsuji

Published Oct 10, 1988• 43 citations
Publisher

Abstract

It is shown that the geometric phase accompanying an arbitrary cyclic change of the state vector can be naturally understood as a canonical phase term in the coherent-state path integral. The adiabatic phase is shown to be derived as a part of the canonical phase.
DOI
10.1103/physrevlett.61.1687

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The definition and interpretation of canonical, phase space path integrals has evolved over many years to achieve a form that now admits a correct and rigorous formulation, which is also covariant under canonical coordinate transformations. Such formulations involve coherent state representations, which, in their modern version, were originally introduced as an alternative tool to construct phase space path integrals. Moreover, coherent state representations lead to physical interpretations that are more natural than those afforded by more traditional representations. Suitable continuous time regularization procedures lead to a covariant phase space path integral formulation that greatly clarifies the vague phrase that canonical quantization requires Cartesian coordinates.