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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Klauder, J.R. Coherent State Path Integrals Without Resolutions of Unity. Foundations of Physics 31, 57–67 (2001). https://doi.org/10.1023/A:1004151804452
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DOI: https://doi.org/10.1023/A:1004151804452