On the Path-Integral Derivation of the Anomaly for the Hermitian Equivalent of the Complex $PT$-Symmetric Quartic Hamiltonian

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dc.creatorJones, H. F.
dc.creatorMateo, J.
dc.creatorRivers, R. J.
dc.date2006-10-23
dc.date.accessioned2026-07-07T11:28:05Z
dc.date.available2026-07-07T11:28:05Z
dc.descriptionIt can be shown using operator techniques that the non-Hermitian $PT$-symmetric quantum mechanical Hamiltonian with a "wrong-sign" quartic potential $-gx^4$ is equivalent to a Hermitian Hamiltonian with a positive quartic potential together with a linear term. A naive derivation of the same result in the path-integral approach misses this linear term. In a recent paper by Bender et al. it was pointed out that this term was in the nature of a parity anomaly and a more careful, discretized treatment of the path integral appeared to reproduce it successfully. However, on re-examination of this derivation we find that a yet more careful treatment is necessary, keeping terms that were ignored in that paper. An alternative, much simpler derivation is given using the additional potential that has been shown to appear whenever a change of variables to curvilinear coordinates is made in a functional integral.
dc.descriptionLaTeX, 12 pages, no figures
dc.identifierhttps://arxiv.org/abs/hep-th/0610245
dc.identifierhttp://arxiv.org/abs/hep-th/0610245
dc.identifierPhys.Rev.D74:125022,2006
dc.identifierdoi:10.1103/PhysRevD.74.125022
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/196328
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Physics
dc.titleOn the Path-Integral Derivation of the Anomaly for the Hermitian Equivalent of the Complex $PT$-Symmetric Quartic Hamiltonian
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