Semiclassical Quantization Condition for the Energy Levels of a Relativistic Two-Fermion System

New semiclassical quantization conditions for the energy levels of pseudoscalar, vector, and pseudovector mesons as composite systems formed by two relativistic arbitrary-mass fermions interacting both via nonsingular confining potentials and singular confining funnel-type potentials involving Coulomb (chromodynamical) interaction were derived. The respective analysis was performed within the relativistic quasipotential approach based on the covariant Hamiltonian formulation of quantum field theory via a transition from the momentum representation in Lobachevsky space to the three-dimensional configuration representation for the case of a composite system of two relativistic spin particles that have arbitrary masses.

Automated summary

New semiclassical quantization conditions for the energy levels of pseudoscalar, vector, and pseudovector mesons as composite systems were derived. These conditions are applicable to the composite systems formed by two relativistic arbitrary-mass fermions interacting via nonsingular confining potentials and singular confining funnel-type potentials involving Coulomb interaction.