Ordinary versus PT-symmetric Φ³ quantum field theory

Journal Article · Mon Apr 02 00:00:00 EDT 2012 · Physical Review. D, Particles, Fields, Gravitation and Cosmology

DOI:https://doi.org/10.1103/PhysRevD.85.085001· OSTI ID:1098638

Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele

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.

• Sponsoring Organization: USDOE
• OSTI ID: 1098638
• Journal Information: Physical Review. D, Particles, Fields, Gravitation and Cosmology, Journal Name: Physical Review. D, Particles, Fields, Gravitation and Cosmology Vol. 85 Journal Issue: 8; ISSN 1550-7998
• Publisher: American Physical Society
• Country of Publication: United States
• Language: English