TITLE:
Hermitian vs PT-Symmetric Scalar Yukawa Model
AUTHORS:
Vladimir E. Rochev
KEYWORDS:
Scalar Field Theory, Non-Hermitian Lagrangians, Schwinger-Dyson Equations, Asymptotic Behavior
JOURNAL NAME:
Journal of Modern Physics,
Vol.7 No.9,
May
23,
2016
ABSTRACT: A comparative analysis of a model of complex scalar field φ and real scalar field χ with interaction for the real and purely imaginary values of coupling g in perturbative and non-perturbative regions is provided. In contrast to the usual Hermitian version (real g), which is asymptotically free and energetically unstable, the non-Hermitian PT-symmetric theory (imaginary g) is energetically stable and not asymptotically free. The non-perturbative approach based on Schwinger-Dyson equations reveals new interesting feature of the non-Hermitian model. While in the Hermitian version of theory the phion propagator has the non-physical non-isolated singularity in the Euclidean region of momenta, the non-Hermitian theory substantially free of this drawback, as the singularity moves in the pseudo-Euclidean region.