scholarly journals A q-deformation of true-polyanalytic Bargmann transforms when q -1 >1

2022 ◽  
Vol 359 (10) ◽  
pp. 1295-1305
Author(s):  
Othmane El Moize ◽  
Zouhaïr Mouayn
Keyword(s):  
Bargmann Transforms

Non-trivial 1d and 2d Segal–Bargmann transforms

2019 ◽  
Vol 30 (7) ◽  
pp. 547-563 ◽  
Author(s):  
Abdelhadi Benahmadi ◽  
Allal Ghanmi
Keyword(s):  
Bargmann Transforms

THE μ-DEFORMED SEGAL–BARGMANN TRANSFORM IS A HALL TYPE TRANSFORM

2009 ◽  
Vol 12 (02) ◽  
pp. 269-289 ◽  
Author(s):  
STEPHEN BRUCE SONTZ
Keyword(s):  
Analytic Continuation ◽  
Heat Kernel ◽  
Bargmann Transform ◽  
Kernel Analysis ◽  
Bargmann Transforms ◽  
Heat Kernel Analysis

We present an explanation of how the μ-deformed Segal–Bargmann spaces, that are studied in various articles of the author in collaboration with Angulo, Echavarría and Pita, can be viewed as deserving their name, that is, how they should be considered as a part of Segal–Bargmann analysis. This explanation relates the μ-deformed Segal–Bargmann transforms to the generalized Segal–Bargmann transforms introduced by B. Hall using heat kernel analysis. All the versions of the μ-deformed Segal–Bargmann transform can be understood as Hall type transforms. In particular, we define a μ-deformation of Hall's "Version C" generalized Segal–Bargmann transform which is then shown to be a μ-deformed convolution with a μ-deformed heat kernel followed by analytic continuation. Our results are generalizations and analogues of the results of Hall.

scholarly journals Polyanalytic relativistic second Bargmann transforms

2015 ◽  
Vol 56 (5) ◽  
pp. 053501 ◽  
Author(s):  
Zouhaïr Mouayn
Keyword(s):  
Bargmann Transforms

scholarly journals Compositions of states and observables in Fock spaces

2019 ◽  
Vol 32 (05) ◽  
pp. 2050012
Author(s):  
L. Amour ◽  
L. Jager ◽  
J. Nourrigat
Keyword(s):  
Quantum Electrodynamics ◽  
Fock Space ◽  
The Other ◽  
Wick Product ◽  
Fock Spaces ◽  
Weyl Symbol ◽  
Time Dynamics ◽  
Bargmann Transforms ◽  
Identification Operator

This article is concerned with compositions in the context of three standard quantizations in the framework of Fock spaces, namely, anti-Wick, Wick and Weyl quantizations. The first one is a composition of states also known as a Wick product and is closely related to the standard scattering identification operator encountered in Quantum Electrodynamics for issues on time dynamics (see [ 29 , 13 ]). Anti-Wick quantization and Segal–Bargmann transforms are implied here for that purpose. The other compositions are for observables (operators in some specific classes) for the Wick and Weyl symbols. For the Wick and Weyl symbols of the composition of two operators, we obtain an absolutely converging series and for the Weyl symbol, the remainder terms up to any orders of the expansion are controlled, still in the Fock space framework.

scholarly journals Generalized Second Bargmann Transforms Associated with the Hyperbolic Landau Levels on the Poincaré Disk

2011 ◽  
Vol 13 (3) ◽  
pp. 513-524 ◽  
Author(s):  
Fouzia El Wassouli ◽  
Allal Ghanmi ◽  
Ahmed Intissar ◽  
Zouhaïr Mouayn
Keyword(s):  
Landau Levels ◽  
Bargmann Transforms ◽  
Poincaré Disk

scholarly journals The -Version Segal-Bargmann Transform for Finite Coxeter Groups Defined by the Restriction Principle

2011 ◽  
Vol 2011 ◽  
pp. 1-23 ◽  
Author(s):  
Stephen Bruce Sontz
Keyword(s):  
Coxeter Group ◽  
Coxeter Groups ◽  
Reproducing Kernel ◽  
Basic Result ◽  
Bargmann Transform ◽  
Restriction Principle ◽  
Finite Coxeter Group ◽  
Bargmann Transforms ◽  
Definition Of ◽  
Special Case

We apply a special case, the restriction principle (for which we give a definition simpler than the usual one), of a basic result in functional analysis (the polar decomposition of an operator) in order to define , the -version of the Segal-Bargmann transform, associated with a finite Coxeter group acting in and a given value of Planck's constant, where is a multiplicity function on the roots defining the Coxeter group. Then we immediately prove that is a unitary isomorphism. To accomplish this we identify the reproducing kernel function of the appropriate Hilbert space of holomorphic functions. As a consequence we prove that the Segal-Bargmann transforms for Versions , , and are also unitary isomorphisms though not by a direct application of the restriction principle. The point is that the -version is the only version where a restriction principle, in our definition of this method, applies directly. This reinforces the idea that the -version is the most fundamental, most natural version of the Segal-Bargmann transform.

scholarly journals Segal-Bargmann transforms from hyperbolic Hamiltonians

2021 ◽  
pp. 125146
Author(s):  
William D. Kirwin ◽  
José Mourão ◽  
João P. Nunes ◽  
Thomas Thiemann
Keyword(s):  
Bargmann Transforms
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