Bethe-Salpeter Bound-State Solutions: Examining Semirelativistic Approaches

• URL: http://arxiv.org/abs/2210.07720v1
• Date: Fri, 14 Oct 2022 11:37:21 GMT
• Title: Bethe-Salpeter Bound-State Solutions: Examining Semirelativistic Approaches
• Authors: Wolfgang Lucha
• Abstract summary: A framework for the description of two-particle bound states is provided by the Poincar'e-covariant homogeneous Bethe-Salpeter equation. A coarse idea of the bound-state spectrum to be expected might be gained by adhering to some simplifying approximations. The reliability of the insights inferred from the arising simpler bound-state equation may be straightforwardly examined.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Within the formalism of relativistic quantum field theory an adequate framework for the description of two-particle bound states, such as, for instance, all conventional (i.e., non-exotic) mesons, is provided by the Poincar\'e-covariant homogeneous Bethe-Salpeter equation. In applications, however, this approach usually proves to be rather involved, whence it is not always quite easy to extract the predictions sought. In view of this, a coarse idea of the bound-state spectrum to be expected might be gained by adhering to some simplifying approximations - which constitutes an entirely legitimate first step. The reliability of the insights inferred from the arising simpler bound-state equation may be straightforwardly examined by taking into account a couple of rigorous constraints on the obtained discrete spectrum. Application of these tools is illustrated for popular potentials.

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