Abstract
-symmetric quantum mechanics began with a study of the Hamiltonian . A surprising feature of this non-Hermitian Hamiltonian is that its eigenvalues are discrete, real, and positive when . This paper examines the corresponding quantum-field-theoretic Hamiltonian in -dimensional spacetime, where is a pseudoscalar field. It is shown how to calculate the Green’s functions as series in powers of directly from the Euclidean partition function. Exact finite expressions for the vacuum energy density, all of the connected -point Green’s functions, and the renormalized mass to order are derived for . For the one-point Green’s function and the renormalized mass are divergent, but perturbative renormalization can be performed. The remarkable spectral properties of -symmetric quantum mechanics appear to persist in -symmetric quantum field theory.
- Received 29 October 2018
DOI:https://doi.org/10.1103/PhysRevD.98.125003
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Published by the American Physical Society