6533b855fe1ef96bd12afdb9
RESEARCH PRODUCT
Quantizations from reproducing kernel spaces
Fabio BagarelloS. Twareque AliJean-pierre Gazeausubject
[PHYS]Physics [physics]PhysicsPure mathematicsHermite polynomials010102 general mathematicsSpectrum (functional analysis)FOS: Physical sciencesGeneral Physics and AstronomyMathematical Physics (math-ph)coherent states16. Peace & justice01 natural sciencesLinear subspaceQuantization (physics)Kernel (statistics)0103 physical sciencesCoherent statesCommutation0101 mathematics[PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph]010306 general physicsSettore MAT/07 - Fisica MatematicaMathematical PhysicsComputingMilieux_MISCELLANEOUSHarmonic oscillatordescription
Abstract The purpose of this work is to explore the existence and properties of reproducing kernel Hilbert subspaces of L 2 ( C , d 2 z / π ) based on subsets of complex Hermite polynomials. The resulting coherent states (CS) form a family depending on a nonnegative parameter s . We examine some interesting issues, mainly related to CS quantization, like the existence of the usual harmonic oscillator spectrum despite the absence of canonical commutation rules. The question of mathematical and physical equivalences between the s -dependent quantizations is also considered.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-05-01 | Annals of Physics |