## Abstract

PT-symmetric quantum mechanics began with a study of the Hamiltonian H=p2+x2(ix)μ. A surprising feature of this non-Hermitian Hamiltonian is that its eigenvalues are discrete, real, and positive when μ≥0. This paper examines the corresponding quantum-field-theoretic Hamiltonian H=12( φ)2+12φ2(iφ)μ in D-dimensional spacetime, where φ is a pseudoscalar field. It is shown how to calculate the Green's functions as series in powers of μ directly from the Euclidean partition function. Exact finite expressions for the vacuum energy density, all of the connected n-point Green's functions, and the renormalized mass to order μ are derived for 0≤D<2. For D≥2 the one-point Green's function and the renormalized mass are divergent, but perturbative renormalization can be performed. The remarkable spectral properties of PT-symmetric quantum mechanics appear to persist in PT-symmetric quantum field theory.

Original language | English |
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Article number | 125003 |

Pages (from-to) | 1-9 |

Journal | Physical Review D |

Volume | 98 |

Issue number | 12 |

Early online date | 13 Dec 2018 |

DOIs | |

Publication status | Published - 15 Dec 2018 |