Pt-symmetry and its spontaneous breakdown explained by anti-linearity

Abstract

The impact of an anti-unitary symmetry on the spectrum of non-Hermitian operators is studied. Wigner's normal form of an anti-unitary operator accounts for the spectral properties of non-Hermitian, PT-symmetric Hamiltonians. The occurrence of either single real or complex conjugate pairs of eigenvalues follows from this theory. The corresponding energy eigenstates span either one- or two-dimensional irreducible representations of the symmetry PT. In this framework, the concept of a spontaneously broken PT-symmetry is not needed.