Hermitian vs PT-Symmetric Scalar Yukawa Model

الأصل · EN

A comparative analysis of a model of complex scalar field ϕ and real scalar field χ with interaction gϕ*ϕχ for the real and purely imaginary values of coupling g in perturbative and non-perturbative regions. 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 singulatity moves in the pseudo-Euclidean region.