PT-symmetric quantum field theory in D dimensions
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 ϵ≥0. This paper examines the corresponding quantum-field-theoretic Hamiltonian H=12(∇ϕ)2+12ϕ2(iϕ)ϵ i...
Gespeichert in:
| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
13 December 2018
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| In: |
Physical review
Year: 2018, Jahrgang: 98, Heft: 12 |
| ISSN: | 2470-0029 |
| DOI: | 10.1103/PhysRevD.98.125003 |
| Online-Zugang: | Verlag, Volltext: http://dx.doi.org/10.1103/PhysRevD.98.125003 Verlag, Volltext: https://link.aps.org/doi/10.1103/PhysRevD.98.125003 
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| Verfasserangaben: | Carl M. Bender, Nima Hassanpour, S.P. Klevansky, and Sarben Sarka |
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| 520 | |a 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 ϵ≥0. 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 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. | ||
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