Reproducing kernel Hilbert spaces and extremal problems for scattering of particles with arbitrary spins
type: Item
instance of: scholarly article
title: Reproducing kernel Hilbert spaces and extremal problems for scattering of particles with arbitrary spins
zbMATH Open document ID: 0608.47010
DOI: 10.1007/BF00670335
author: D. B. Ion
published in: International Journal of Theoretical Physics
publication date: 1985-01-01T00:00:00Z
review text: In this paper each helicity amplitude of the two-body scattering of particles with arbitrary spins is considered as an element of a special class of Hilbert spaces \(H^{[\mu]}\). This space, which is called reproducing kernel Hilbert space (RKHS) has many special properties that appear to make it a natural space of functions to associate with the scattering helicity amplitudes. Some of the special properties of the RKHS are developed and then used to characterization of reproducing kernel (RK) of \(H^{[\mu]}\) as the solution to certain extremal problems. Then, it was shown that the optimal scattering state from the RKHS of the helicity amplitudes is analogous to the coherent state from the RKHS of the wave functions. The essential characteristic features of the scattering of particles with arbitrary spins in the optimal state dominance limit are established. An important alternative to the partial wave helicity analysis in terms of a fundamental set of optimal states is presented.
Mathematics Subject Classification ID: 47A40
Mathematics Subject Classification ID: 46E20
Mathematics Subject Classification ID: 81U05
zbMATH DE Number: 3983908
zbMATH Keywords: helicity amplitude
zbMATH Keywords: two-body scattering of particles with arbitrary spins
zbMATH Keywords: reproducing kernel Hilbert space
zbMATH Keywords: extremal problems
zbMATH Keywords: optimal scattering state
zbMATH Keywords: coherent state
zbMATH Keywords: optimal state dominance limit
zbMATH Keywords: partial wave helicity analysis
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00670335
OpenAlex ID: W1973542533
description: scientific article; zbMATH DE number 3983908