The Heisenberg–Weyl group in the coherent state basis and the Bargmann transform

DOI10.1063/1.527888zbMath0649.46067OpenAlexW2066611981MaRDI QIDQ3794753

Debabrata Basu, Tapan Kumar Kar

Publication date: 1988

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.527888

zbMATH Keywords

integral transformBargmann transformrepresentation matricesBargmann's Hilbert space of analytic functionscoherent state wave functionsintegral kernel of Bargmanninversion of the transform

Mathematics Subject Classification ID

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Hilbert spaces of continuous, differentiable or analytic functions (46E20) Miscellaneous applications of functional analysis (46N99)

Related Items (2)

Hilbert spaces of analytic functions for the SL(2,R) coherent states and a class of associated integral transforms ⋮ Representations of SL(2,R) in a Hilbert space of analytic functions and a class of associated integral transforms

Cites Work

• The action option and a Feynman quantization of spinor fields in terms of ordinary \(C\)-numbers
• New 'coherent' states associated with non-compact groups
• UNITARY REPRESENTATIONS OF NILPOTENT LIE GROUPS
• On a Hilbert space of analytic functions and an associated integral transform part I
• The metaplectic group within the Heisenberg–Weyl ring
• Equivalence of Semiclassical and Quantum Mechanical Descriptions of Statistical Light Beams

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