Weak Coherent States and their Path Integrals

Details Weak Coherent States and their Path Integrals Weak Coherent States and their Path Integrals

2003-08-27

arxiv.org/abs/hep-th/0308185v1

Physics

High Energy Physics

High Energy Physics - Theory

104 pages, 2 figures

Scientific paper

Weak coherent states share many properties of the usual coherent states, but do not admit a resolution of unity expressed in terms of a local integral. They arise e.g. in the case that a group acts on an inadmissible fiducial vector. Motivated by the recent Affine Quantum Gravity Program, the present work studies the path integral representation of the affine weak coherent state matrix elements of the unitary time-evolution operator. Since weak coherent states do not admit a resolution of unity, it is clear that the standard way of constructing a path integral, by time slicing, is predestined to fail. Instead, a well-defined path integral with Wiener measure, based on a continuous-time regularization, is used to approach this problem. The dynamics is rigorously established for linear Hamiltonians, and the difficulties presented by more general Hamiltonians are addressed.

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