211 research outputs found
On the phase structure of vector-matrix scalar model in four dimensions
The leading-order equations of the -- expansion for a vector-matrix
model with interaction in four dimensions are
investigated. This investigation shows a change of the asymptotic behavior in
the deep Euclidean region in a vicinity of a certain critical value of the
coupling constant. For small values of the coupling the phion propagator
behaves as free. In the strong-coupling region the asymptotic behavior
drastically changes -- the propagator in the deep Euclidean region tend to some
constant limit. The phion propagator in the coordinate space has a
characteristic shell structure. At the critical value of coupling that
separates the weak and strong coupling regions, the asymptotic behavior of the
phion propagator is a medium among the free behavior and the constant--type
behavior in strong--coupling region. The equation for a vertex with zero
transfer is also investigated. The asymptotic behavior of the solutions shows
the finiteness of the charge renormalization constant. In the strong-coupling
region, the solution for the vertex has the same shell structure in coordinate
space as the phion propagator. An analogy between the phase transition in this
model and the re-arrangement of the physical vacuum in the supercritical
external field due to the "fall-on-the-center" phenomenon is discussed.Comment: 7 page
On solving Schwinger-Dyson equations for non-Abelian gauge theory
A method for solving Schwinger-Dyson equations for the Green function
generating functional of non-Abelian gauge theory is proposed. The method is
based on an approximation of Schwinger-Dyson equations by exactly soluble
equations. For the SU(2) model the first step equations of the iteration scheme
are solved which define a gauge field propagator. Apart from the usual
perturbative solution, a non-perturbative solution is found which corresponds
to the spontaneous symmetry breaking and obeys infrared finite behaviour of the
propagator.Comment: 12 pages, Plain LaTeX, no figures, extended and revised version
published in Journal of Physics
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