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Description
In this contribution the solution of the Schwinger-Dyson equation in Minkowski space, for a QED-like theory with a massive vector, in Rainbow ladder approximation and using integral representation will be presented for the Feynman gauge and compared to Euclidean results with Pauli-Villars regulators. The unregulated equations have solution below the critical coupling constant $\alpha_c= \frac{\pi}{4}$ before the Miransky scaling takes place. It is derived the power-law form of the spectral densities for $\alpha<\alpha_c$. It will be also discussed an analogous property, known for the Bethe-Salpeter equation applied to the fermion-fermion case, where for the stability of the bound state solution the coupling constant should be below a critical value due to the breaking of scale invariance, which will be discussed in the context of a fermion-boson BSE with vector exchange. The power law behavior of the asymptotic light-cone amplitudes will be compared to numerical results from the solution of the BSE in Minkowski space.
This contribution has the collaboration of J. H. de Alvarenga Nogueira, D. C. Duarte, S. Jia, P. Maris, W. de Paula, E. Pace, G. Salmè, and E. Ydrefors.
