2013/02/28 by Vladimir E. Rochev, V E Rochev
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Advanced Operator Algebra Research #Coupling constant #Critical point (mathematics) #Euclidean geometry #Integral equation #Nonlinear system #Propagator #Scalar (mathematics) #Scalar field #Spectral Theory in Mathematical Physics #Yukawa potential #hep-ph #hep-th #nucl-th
paper · pdf · doi:10.1088/1751-8113/46/18/185401
published as J.Phys.A:Math.Theor.46 (2013) 185401 · 19 pages; some points clarified; typos corrected
openalex publication_date 2013/04/19 · arxiv created 2013/04/29 · arxiv updated 2015/06/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A sequence of n -particle approximations for the system of Schwinger–Dyson equations is investigated in the model of a complex scalar field ϕ and a real scalar field χ with the interaction g ϕ*ϕχ. 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 exists, which separates the weak- and strong-coupling regions with the different asymptotic behavior for deep Euclidean momenta. In the weak-coupling region ( ), the propagators are asymptotically free, which corresponds to the wide-spread opinion about the dominance of perturbation theory for this model. At the critical point, the asymptotics of propagators are ∼1/ p . In the strong-coupling region ( ), 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.