1302.1311 (Vladimir E. Rochev)

Asymptotic behavior and critical coupling in the scalar Yukawa model
from Schwinger-Dyson equations    [PDF]

Vladimir E. Rochev

A sequence of $n$-particle approximations for the system of Schwinger-Dyson equations is investigated in the model of complex scalar field $\phi$ and real scalar field $\chi$ with interaction $g\phi^*\phi\chi$. In the first non-trivial two-particle approximation the system is reduced to a system of two nonlinear integral equations for propagators. The study of this system shows that for equal masses a critical coupling constant $g^2_c$ exists, which separates the weak- and strong-coupling regions with the different asymptotic behavior for deep Euclidean momenta. In the weak-coupling region ($g^2g^2_c$) the propagators are asymptotically constant, which corresponds to the ultra-local limit. For unequal masses the critical point transforms into a segment of values, in which there are no solutions with a self-consistent ultraviolet behavior without Landau singularities.

View original: http://arxiv.org/abs/1302.1311