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Volume 13
Issue 24
10.3390/math13243916
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Article

Planar Dirac Equation with Radial Contact Potentials

by
José Tadeu Lunardi
1,
Sergio Salamanca
2,
Javier Negro
2 and
Luis Miguel Nieto
2,*
1
Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, Ponta Grossa 84320-900, PR, Brazil
2
Departamento de Física Teórica, Atómica y Óptica, Laboratory for Disruptive Interdisciplinary Science (LaDIS), Universidad de Valladolid, 47011 Valladolid, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(24), 3916; https://doi.org/10.3390/math13243916 (registering DOI)
Submission received: 11 November 2025 / Revised: 2 December 2025 / Accepted: 3 December 2025 / Published: 7 December 2025
(This article belongs to the Section E4: Mathematical Physics)
Versions Notes

Abstract

We investigate the planar Dirac equation with the most general time-independent contact (singular) potential supported on a circumference. Taking advantage of the radial symmetry, the problem is effectively reduced to a one-dimensional one (the radial), and the contact potential is addressed in a mathematically rigorous way using a distributional approach that was originally developed to treat point interactions in one dimension, providing a physical interpretation for the interaction parameters. The most general contact interaction for this system is obtained in terms of four physical parameters: the strengths of a scalar and the three components of a singular Lorentz vector potential supported on the circumference. We then investigate the bound and scattering solutions for several choices of the physical parameters, and analyze the confinement properties of the corresponding potentials.
Keywords: Dirac equation; Dirac materials; contact potentials; Schwartz’s theory of distributions; confining potentials; resonances Dirac equation; Dirac materials; contact potentials; Schwartz’s theory of distributions; confining potentials; resonances

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MDPI and ACS Style

Lunardi, J.T.; Salamanca, S.; Negro, J.; Nieto, L.M. Planar Dirac Equation with Radial Contact Potentials. Mathematics 2025, 13, 3916. https://doi.org/10.3390/math13243916

AMA Style

Lunardi JT, Salamanca S, Negro J, Nieto LM. Planar Dirac Equation with Radial Contact Potentials. Mathematics. 2025; 13(24):3916. https://doi.org/10.3390/math13243916

Chicago/Turabian Style

Lunardi, José Tadeu, Sergio Salamanca, Javier Negro, and Luis Miguel Nieto. 2025. "Planar Dirac Equation with Radial Contact Potentials" Mathematics 13, no. 24: 3916. https://doi.org/10.3390/math13243916

APA Style

Lunardi, J. T., Salamanca, S., Negro, J., & Nieto, L. M. (2025). Planar Dirac Equation with Radial Contact Potentials. Mathematics, 13(24), 3916. https://doi.org/10.3390/math13243916

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