Ordinary versus PT-symmetric Φ³ quantum field theory
Abstract
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric igΦ³ quantum field theory. This quantum field theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.
- Authors:
- Publication Date:
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1098638
- Resource Type:
- Publisher's Accepted Manuscript
- Journal Name:
- Physical Review. D, Particles, Fields, Gravitation and Cosmology
- Additional Journal Information:
- Journal Name: Physical Review. D, Particles, Fields, Gravitation and Cosmology Journal Volume: 85 Journal Issue: 8; Journal ID: ISSN 1550-7998
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
Citation Formats
Bender, Carl M., Branchina, Vincenzo, and Messina, Emanuele. Ordinary versus PT-symmetric Φ³ quantum field theory. United States: N. p., 2012.
Web. doi:10.1103/PhysRevD.85.085001.
Bender, Carl M., Branchina, Vincenzo, & Messina, Emanuele. Ordinary versus PT-symmetric Φ³ quantum field theory. United States. https://doi.org/10.1103/PhysRevD.85.085001
Bender, Carl M., Branchina, Vincenzo, and Messina, Emanuele. Mon .
"Ordinary versus PT-symmetric Φ³ quantum field theory". United States. https://doi.org/10.1103/PhysRevD.85.085001.
@article{osti_1098638,
title = {Ordinary versus PT-symmetric Φ³ quantum field theory},
author = {Bender, Carl M. and Branchina, Vincenzo and Messina, Emanuele},
abstractNote = {A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric igΦ³ quantum field theory. This quantum field theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.},
doi = {10.1103/PhysRevD.85.085001},
journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},
number = 8,
volume = 85,
place = {United States},
year = {Mon Apr 02 00:00:00 EDT 2012},
month = {Mon Apr 02 00:00:00 EDT 2012}
}
https://doi.org/10.1103/PhysRevD.85.085001
Web of Science
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