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Yukawa's old bilocal field theory, with modernization in the treatment of"relative time," can describe a relativistic bound state of chiral fermions.This connects to bosonized effective chiral Lagrangians and theNambu-Jona-Lasinio (NJL) model, providing a description of the internaldynamics of the bound states. It features a static internal wave-function,$\phi(\vec{r})$, in the center-of-mass frame that satisfies aSchr\"odinger-Klein-Gordon equation with eigenvalues $m^2$. We analyze the"coloron" model (single perturbative massive gluon exchange) which yields a UVcompletion of the NJL model. This has a BCS-like enhancement of itsinteraction, $\propto N_c$, the number of colors. It is classically critical,with $g_{critical}$ remarkably close to the NJL quantum critical coupling.Negative eigenvalues for $m^2$ lead to spontaneous symmetry breaking, and theYukawa coupling of the bound state to constituent fermions is emergent.

Revisiting Yukawa's Bilocal Field Theory for Composite Scalar Bosons