Hermitian vs <i>PT</i>-Symmetric Scalar Yukawa Model

Abstract

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 P Tsymmetric 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.

Goldstone bosons in different PT-regimes of non-Hermitian scalar quantum field theories

“…Naturally, as a direct extension of the well studied purely complex cubic potential in quantum mechanics the scalar field theory with imaginary cubic self-interaction term iφ 3 has been investigated at first [10,11] and also the more generally deformed harmonic oscillator has been generalised to a field theoretical interaction term φ 2 (iφ) ε more recently [12]. Non-Hermitian versions with a field theoretic Yukawa interaction [13,14,15,16] have been investigated in regard to Higgs boson decay. Besides bosonic theories also generalizations to non-Hermitian fermion theories such as a free fermion theory with a γ 5mass term or the massive Thirring model have been proposed [17].…”

Pseudo-Hermitian approach to Goldstone’s theorem in non-Abelian non-Hermitian quantum field theories

“…The extension from quantum field theories with Hermitian actions to those with a non-Hermitian actions has been addressed recently for various concrete systems, such as scalar field theory with imaginary cubic self-interaction terms [1,2], field theoretical analogues to the deformed harmonic oscillator [3], non-Hermitian versions with a field theoretic Yukawa interaction [4,5,6,7], free fermion theory with a γ 5 -mass term and the massive Thirring model [8], PT -symmetric versions of quantum electrodynamics [9,10] and PT -symmetric quantum field theories in higher dimensions [11].…”

The Yukawa Model in One Space - One Time Dimensions

“…In particle physics, Yukawa's interaction or Yukawa coupling, is an interaction between a scalar field φ and a Dirac field ψ of the type V = g ψφψ for a scalar field or V = g ψiγ 5 φψ for a pseudoscalar field, g is called a Yukawa coupling constant. Recently the scalar Yukawa model has been introduced, where the Dirac field is replaced by a complex scalar field [2][3][4]. The Yukawa interaction is also used in the Standard Model to describe the coupling between the Higgs field and massless quark and lepton fields (i.e., the fundamental fermion particles).…”