On the noncommutative eikonal
J.M. Isidro, P. Fernandez de Cordoba, J.M. Rivera-Rebolledo, J.L.G., Santander
TL;DR
This paper explores the eikonal approximation in quantum mechanics on the Moyal plane using operator-valued wavefunctions, offering a novel approach that avoids star products and handles noncommuting coordinates.
Contribution
It introduces a new operator-based framework for the eikonal approximation on noncommutative spaces, bypassing traditional star product methods.
Findings
Develops an operator-valued wavefunction formalism for the Moyal plane
Provides insights into quantum mechanics in noncommutative geometries
Offers potential applications in noncommutative quantum theories
Abstract
We study the eikonal approximation to quantum mechanics on the Moyal plane. Instead of using a star product, the analysis is carried out in terms of operator-valued wavefunctions depending on noncommuting, operator-valued coordinates.
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