2015/12/10 by V. E. Rochev, Rochev, V. E.
Physics and Astronomy · #Astrophysics and Cosmic Phenomena #Experimental and Theoretical Physics Studies #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Mechanics and Non-Hermitian Physics #hep-th
paper · pdf · doi:10.48550/arxiv.1512.03286
11 pages
arxiv created 2015/12/10 · openalex publication_date 2015/12/10 · arxiv updated 2015/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.