Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Springer eBooks

Resolutions of the Identity in Terms of Line Integrals of Coherent States and Their Use for Quantum State Engineering

Apostol Vourdas

Published Jan 1, 1997• 0 citations
Publisher
DOI
10.1007/978-1-4615-5923-8_28

Related papers

Coherent State Path Integrals Without Resolutions of Unity

John R. Klauder

arXiv:quant-ph/0008132•Foundations of Physics•Jan 1, 2001•11 citations

Resolutions of the identity in terms of SU(2) coherent states and their use for quantum-state engineering

Apostol Vourdas

Resolutions of the identity in terms of line integrals that involve SU(2) coherent states and their complementary states are presented. They are used for the expansion of various states in terms of SU(2) coherent states on a line. The properties of the complementary states are also studied. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Nov 1, 1996•14 citations

Connection between coherent states and some integrals and integral representations

Dušan Popov

arXiv:2408.10749•Reports on Mathematical Physics•Feb 1, 2026•0 citations

Resolutions of the identity in terms of line integrals ofSU(1, 1) coherent states

Apostol Vourdas, Alfred Wünsche

Resolutions of the identity in terms of contour integrals that involve coherent states and their `complementary states', are derived. The complementary states are auxiliary states that help in the formulation of these resolutions of the identity. Since the coherent states are normalizable inside the unit disc and the complementary states are normalizable outside the unit disc, enlargements of the Hilbert space are considered which allow the construction of resolutions of the identity in terms of contour integrals in rings . Several examples of our formalism are presented.

Journal of Physics A Mathematical and General•Nov 20, 1998•18 citations

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

Ryo Namiki

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.

arXiv:2402.08317•Feb 13, 2024•0 citations

Coherent States and Applications in Mathematical Physics

Monique Combescure, Didier Robert

Theoretical and mathematical physics•Jan 1, 2012•232 citations
Resolutions of the identity in terms of contour integrals that involve coherent states and their `complementary states', are derived. The complementary states are auxiliary states that help in the formulation of these resolutions of the identity. Since the coherent states are normalizable inside the unit disc and the complementary states are normalizable outside the unit disc, enlargements of the Hilbert space are considered which allow the construction of resolutions of the identity in terms of contour integrals in rings . Several examples of our formalism are presented.
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.