π,K, ρ, φ asqq¯bound states of the Salpeter equation in a3P0condensed vacuum

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Abstract
With the help of the Feynman rules, we derive and solve the Salpeter equation (in the presence of the condensed vacuum) for the mesonic bound states π, K, ρ, and φ. For these mesons, we give wave functions and bare masses (that is, prior to decay). For S waves, Gaussian approximations—the cluster sizes—are also given. These cluster sizes depend on the chiral angle. Whereas pseudo- scalar wave functions are shown to behave like doublets in an abstract spinlike energy space, vectorial mesons are shown to possess a more complicated structure involving couplings to spatial excitations as well. Already at this stage it is shown that, in order to accommodate decays, we face strong bounds on the possible values for the potential strength and quark current masses.