Equivalence of a Complex $\cP\cT$-Symmetric Quartic Hamiltonian and a Hermitian Quartic Hamiltonian with an Anomaly
| dc.creator | Bender, Carl M. | |
| dc.creator | Brody, Dorje C. | |
| dc.creator | Chen, Jun-Hua | |
| dc.creator | Jones, Hugh F. | |
| dc.creator | Milton, Kimball A. | |
| dc.creator | Ogilvie, Michael C. | |
| dc.date | 2006-05-05 | |
| dc.date | 2006-05-08 | |
| dc.date.accessioned | 2026-07-07T10:46:35Z | |
| dc.date.available | 2026-07-07T10:46:35Z | |
| dc.description | In a recent paper Jones and Mateo used operator techniques to show that the non-Hermitian $\cP\cT$-symmetric wrong-sign quartic Hamiltonian $H=\half p^2-gx^4$ has the same spectrum as the conventional Hermitian Hamiltonian $\tilde H=\half p^2+4g x^4-\sqrt{2g} x$. Here, this equivalence is demonstrated very simply by means of differential-equation techniques and, more importantly, by means of functional-integration techniques. It is shown that the linear term in the Hermitian Hamiltonian is anomalous; that is, this linear term has no classical analog. The anomaly arises because of the broken parity symmetry of the original non-Hermitian $\cP\cT$-symmetric Hamiltonian. This anomaly in the Hermitian form of a $\cP\cT$-symmetric quartic Hamiltonian is unchanged if a harmonic term is introduced into $H$. When there is a harmonic term, an immediate physical consequence of the anomaly is the appearance of bound states; if there were no anomaly term, there would be no bound states. Possible extensions of this work to $-ϕ^4$ quantum field theory in higher-dimensional space-time are discussed. | |
| dc.description | 19 pages, 7 figures, corrected references | |
| dc.identifier | https://arxiv.org/abs/hep-th/0605066 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0605066 | |
| dc.identifier | Phys.Rev.D74:025016,2006 | |
| dc.identifier | doi:10.1103/PhysRevD.74.025016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/183283 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Quantum Physics | |
| dc.title | Equivalence of a Complex $\cP\cT$-Symmetric Quartic Hamiltonian and a Hermitian Quartic Hamiltonian with an Anomaly | |
| dc.type | text |