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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access April 23, 2014

A relativistic wave equation with a local kinetic operator and an energy-dependent effective interaction for the study of hadronic systems

Maurizio Sanctis
From the journal Open Physics


We study a fully relativistic, two-body, quadratic wave equation for equal mass interacting particles. With this equation the difficulties related to the use of the square roots in the kinetic energy operators are avoided. An energy-dependent effective interaction, also containing quadratic potential operators, is introduced. For pedagogical reasons, it is previously shown that a similar procedure can be also applied to the well-known case of a one-particle Dirac equation. The relationships of our model with other relativistic approaches are briefly discussed. We show that it is possible to write our equation in a covariant form in any reference frame. A generalization is performed to the case of two particles with different mass. We consider some cases of potentials for which analytic solutions can be obtained. We also study a general numerical procedure for solving our equation taking into account the energy-dependent character of the effective interaction. Hadronic physics represents the most relevant field of application of the present model. For this reason we perform, as an example, specific calculations to study the charmonium spectrum. The results show that the adopted equation is able to reproduce with good accuracy the experimental data.

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Published Online: 2014-4-23
Published in Print: 2014-4-1

© 2014 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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