Problems in PT-symmetric Quantum Field Theory

Abstract

Two problems of PT-symmetric quantum field theory are discussed: In the first part, the D-dimensional quantum field theory with the self-interaction phi^2 (i phi)^epsilon is analyzed. Techniques introduced previously in a first-order study of the perturbative nonlinearity expansion in epsilon, [Phys. Rev. D 98, 125003], are generalized for the application at higher orders and used to determine the expansion coefficients of the ground-state energy density, the p-point Green’s functions, and the effective mass of the theory. The perturbative renormalization of the two-dimensional model is discussed to second order in the nonlinearity expansion and the behavior is contrasted with that in a coupling-constant expansion through a multiple-scale analysis. In the second part, the 3 + 1 dimensional Nambu–Jona-Lasinio model is modified by PT-symmetric and anti-PT-symmetric non-Hermitian bilinears to analyze the role of PT symmetry in fermionic quantum field theory. The generated masses of the fermion as well as the scalar and pseudoscalar mesons are obtained. The study is supplemented by an analysis of the fermion mass in the similarly modified 1 + 1 dimensional chiral Gross-Neveu model.