journal article·2021-11-01Open access

A square-integrable spinor solution to non-interacting Dirac equations

Luca Fabbri, Roberto Cianci, Stefano Vignolo

AIP Advances· Volume 11· Issue 11

Abstract

We consider the Dirac equation written in polar form, without any external potential but equipped with a non-zero tensorial connection, and we find a new type of solution that is localized around the origin with a decreasing exponential behavior in the radial coordinate.
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Research context

OpenAlex topics: Quantum Mechanics and Non-Hermitian Physics · Nonlinear Waves and Solitons · Algebraic and Geometric Analysis

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Affiliations

DIME, Sez. Metodi e Modelli Matematici, Università di Genova , Via all’Opera Pia 15, 16145 Genova, Italy

References (28)

Show source-provided references
1. New exact solutions of the Dirac equation. VII10.1007/bf00893130 ↗
2. The exact solution for the Dirac equation with the Cornell potential10.1007/s00601-013-0766-2 ↗
3. Dirac equation on a curved surface10.1016/j.physleta.2016.07.010 ↗
4. Exact solutions of Dirac equation on a static curved space-time10.1016/j.aop.2018.11.025 ↗
5. Local smoothing estimates for the massless Dirac–Coulomb equation in 2 and 3 dimensions10.1016/j.jfa.2016.04.003 ↗
6. Self-adjoint extensions for the Dirac operator with Coulomb-type spherically symmetric potentials10.1007/s11005-018-1093-9 ↗
7. Discrete spectra for critical Dirac-Coulomb Hamiltonians10.1063/1.5011305 ↗
8. Self-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei10.1007/s13324-018-0219-7 ↗
9. Dirac equation in external vector fields: Separation of variables10.1063/1.528215 ↗
10. Dirac equation in external vector fields: New exact solutions10.1063/1.528567 ↗
11. The angular momentum operator in the Dirac equation10.1088/0143-0807/15/4/006 ↗
12. Separation of variables and exact solution of the Klein–Gordon and Dirac equations in an open universe10.1063/1.1501445 ↗
13. New solutions of the Dirac equation for central fields10.1007/978-94-011-3570-2_4 ↗
14. A. M. Steane, “An introduction to spinors,” arXiv:1312.3824 [math-ph].
15. Spinor symmetries and underlying properties10.1140/epjc/s10052-020-7693-4 ↗
16. 2001
17. Classification of singular spinor fields and other mass dimension one fermions10.1142/s0218271814440027 ↗
18. Introduction des parametres relativistes de Cayley-Klein dans la representation hydrodynamique de l’equation de Dirac
19. A generally-relativistic gauge classification of the Dirac fields10.1142/s021988781650078x ↗
20. Covariant inertial forces for spinors10.1140/epjc/s10052-018-6260-8 ↗
21. Polar solutions with tensorial connection of the spinor equation10.1140/epjc/s10052-019-6709-4 ↗
22. 1995
23. Torsion gravity for Dirac fields10.1142/s0219887817500372 ↗
24. Non-trivial effects of sourceless forces for spinors: Toward an Aharonov–Bohm gravitational effect?10.1140/epjc/s10052-019-7380-5 ↗
25. 2003
26. Abstract formulation of the Cole-Hopf transform
27. Singularity-free spinors in gravity with propagating torsion10.1142/s0217732317502212 ↗
28. Spinors in polar form10.1140/epjp/s13360-021-01351-w ↗