• Open Access

PT-symmetric quantum field theory in D dimensions

Carl M. Bender, Nima Hassanpour, S. P. Klevansky, and Sarben Sarkar
Phys. Rev. D 98, 125003 – Published 13 December 2018

Abstract

PT-symmetric quantum mechanics began with a study of the Hamiltonian H=p2+x2(ix)ϵ. A surprising feature of this non-Hermitian Hamiltonian is that its eigenvalues are discrete, real, and positive when ϵ0. This paper examines the corresponding quantum-field-theoretic Hamiltonian H=12(ϕ)2+12ϕ2(iϕ)ϵ 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 ϵ 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 ϵ are derived for 0D<2. For D2 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.

  • Received 29 October 2018

DOI:https://doi.org/10.1103/PhysRevD.98.125003

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

Carl M. Bender1,3,*, Nima Hassanpour1,†, S. P. Klevansky2,‡, and Sarben Sarkar3,§

  • 1Department of Physics, Washington University, St. Louis, Missouri 63130, USA
  • 2Institut für Theoretische Physik, Universität Heidelberg, 69120 Heidelberg, Germany
  • 3Department of Physics, King’s College London, London WC2R 2LS, United Kingdom

  • *cmb@wustl.edu
  • nimahassanpourghady@wustl.edu
  • spk@physik.uni-heidelberg.de
  • §sarben.sarkar@kcl.ac.uk

Article Text

Click to Expand

References

Click to Expand
Issue

Vol. 98, Iss. 12 — 15 December 2018

Reuse & Permissions
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

×

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×