Asymptotic behavior in the scalar field theory

Abstract

An asymptotic solution of the system of Schwinger-Dyson equations for four-dimensional Euclidean scalar field theory with interaction $\frac{\lambda }{2}({\varphi }^{\ast }\varphi {)}^2$ is obtained. For $\lambda >{\lambda }_{cr}=16{\pi }^2$ the two-particle amplitude has the pathology-free asymptotic behavior at large momenta. For $\lambda <{\lambda }_{cr}$ the amplitude possesses Landau-type singularity.

16 pages; journal version; references added

References in corpus (7)

• Fixed-Point Structure of Scalar Fields
• On the Fixed-Point Structure of Scalar Fields
• Non-Trivial Directions for Scalar Fields
• Precision check on triviality of phi^4 theory by a new simulation method
• Renormalization Group Functions of the ϕ^4 Theory in the Strong Coupling Limit: Analytical Results
• A non-perturbative method of calculation of Green functions
• Asymptotic Behavior of the \Beta Function in the Φ^4 Theory: A Scheme Without Complex Parameters

Cited by in corpus (3)

• On the Question of an Ultraviolet Zero of the Beta Function of the $\lambda ({\vec{\varphi }}^2{)}_4^2$ Theory
• Asymptotic behavior and critical coupling in the scalar Yukawa model from Schwinger-Dyson equations
• Asymptotic behavior in a model with Yukawa interaction from Schwinger-Dyson equations