Coherent State Path Integrals without Resolutions of Unity

John R. Klauder

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arXiv · quant-ph/0008132

Coherent State Path Integrals without Resolutions of Unity

John R. Klauder

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Abstract

From the very beginning, coherent state path integrals have always relied on a coherent state resolution of unity for their construction. By choosing an inadmissible fiducial vector, a set of ``coherent states'' spans the same space but loses its resolution of unity, and for that reason has been called a set of weak coherent states. Despite having no resolution of unity, it is nevertheless shown how the propagator in such a basis may admit a phase-space path integral representation in essentially the same form as if it had a resolution of unity. Our examples are toy models of similar situations that arise in current studies of quantum gravity.

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John R. Klauder. 2000-08-30. Coherent State Path Integrals without Resolutions of Unity. https://arxiv.org/abs/quant-ph/0008132

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