Strong convergence of a resolution of the identity via canonical coherent states

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Detalles Bibliográficos
Autor principal:	Namiki, Ryo
Formato:	Preprint
Publicado:	2024
Materias:	Quantum Physics Mathematical Physics
Acceso en línea:	Acceder al recurso
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_version_	1866909105101209600
author	Namiki, Ryo
author_facet	Namiki, Ryo
contents	A resolution of the identity due to canonical coherent states is often proven in the weak operator topology. However, such a resolution with an integral symbol is typically supposed to hold in the strong operator topology associated with the framework of the spectral theorem. We provide an elementary proof of the strong convergence for the resolution of the identity due to canonical coherent states starting with a mostly familiar setup. Further, we enjoy a different proof and show that the relevant uniform limit does not exist.
format	Preprint
id	arxiv_https___arxiv_org_abs_2402_08317
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Strong convergence of a resolution of the identity via canonical coherent states Namiki, Ryo Quantum Physics Mathematical Physics A resolution of the identity due to canonical coherent states is often proven in the weak operator topology. However, such a resolution with an integral symbol is typically supposed to hold in the strong operator topology associated with the framework of the spectral theorem. We provide an elementary proof of the strong convergence for the resolution of the identity due to canonical coherent states starting with a mostly familiar setup. Further, we enjoy a different proof and show that the relevant uniform limit does not exist.
title	Strong convergence of a resolution of the identity via canonical coherent states
topic	Quantum Physics Mathematical Physics
url	https://arxiv.org/abs/2402.08317

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