Bound states of relativistic nature

Abstract

Bethe-Salpeter equation, for massless exchange and large fine structure constant $\alpha >\pi /4$, in addition to the Balmer series, provides another (abnormal) series of energy levels which are not given by the Schrödinger equation. So strong field can be created by a point-like charge $Z>107$. The nuclei with this charge, though available, they are far from to be point-like that weakens the field. Therefore, the abnormal states of this origin hardly exist. We analyze the more realistic case of exchange by a massive particle when the large value of coupling constant is typical for the strong interaction. It turns out that this interaction still generates a series of abnormal relativistic states. The properties of these solutions are studied. Their existence in nature seems possible.

arXiv comment13 pages, 10 figures, to be published in Proceedings of the International Conference: Nuclear Theory in the Supercomputing Era-2018 (NTSE-2018), Daejeon, South Korea, October 29 - November 2, 2018; eds. A. M. Shirokov and A. I. Mazur. Pacific National University, Khabarovsk, Russia, 2019

References in corpus (6)

• Solving Bethe-Salpeter equation in Minkowski space
• Solving the Bethe-Salpeter Equation for Scalar Theories in Minkowski Space
• Quantitative studies of the homogeneous Bethe-Salpeter Equation in Minkowski space
• Solving the inhomogeneous Bethe-Salpeter Equation in Minkowski space: the zero-energy limit
• Bound state equation for the Nakanishi weight function
• Excited states of the Wick-Cutkosky model with the Nakanishi representation in the Light-Front framework

Cited by in corpus (7)

• Analytic approach to calculations of mass spectra and decay constants of heavy-light quarkonia in the framework of Bethe-Salpeter equation
• Mass spectrum of pseudo-scalar glueballs from a Bethe-Salpeter approach with the rainbow-ladder truncation
• Mass spectra and decay constants of heavy-light axial quarkonia in the framework of Bethe-Salpeter equation
• Radiative decays of heavy-light quarkonia through $M1$, and $E1$ transitions in the framework of Bethe-Salpeter equation
• Hybrid nature of the abnormal solutions of the Bethe-Salpeter equation in the Wick-Cutkosky model
• Abnormal solutions of Bethe--Salpeter equation with massless and massive exchanges
• Abnormal Bound Systems