• Corpus ID: 53650073

On the number of bound states in QED$_3$

@article{Lima2018OnTN,
  title={On the number of bound states in QED\$\_3\$},
  author={Washington de Lima and Oswaldo M. Del Cima and Daniel H. T. Franco},
  journal={arXiv: Mathematical Physics},
  year={2018}
}

• W. D. Lima, O. M. D. Cima, D. Franco
• Published 3 October 2018
• Mathematics, Physics
• arXiv: Mathematical Physics

We establish the consistency conditions for two-particle non relativistic bound states for any three space-time dimensional quantum electrodynamics model (QED$_3$) exhibiting an attractive scattering potential of $K_{_0}$-type, the Bessel-Macdonald function. Initially, we study the self-adjointness of the hamiltonian operator, then by using {\em Seto-type estimates}, an estimate number of two-quantum bound states is derived for any value of the angular momentum. In fact, this result in connection with the condition that guarantees the self-adjointness of the hamiltonian shows that there can always be a number of two-quantum bound states for any ${\rm QED}_3$ model where a $K_{_0}$-type attractive interaction emerges. To the best of our knowledge, this result has not yet been addressed in the literature.