PT-Symmetric Matrix Quantum Mechanics

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dc.creatorMeisinger, Peter N.
dc.creatorOgilvie, Michael C.
dc.date2007-01-23
dc.date.accessioned2026-07-07T07:47:30Z
dc.date.available2026-07-07T07:47:30Z
dc.descriptionRecently developed methods for PT-symmetric models are applied to quantum-mechanical matrix models. We consider in detail the case of potentials of the form $V=-(g/N^{p/2-1})Tr(iM)^{p}$ and show how the calculation of all singlet wave functions can be reduced to solving a one-dimensional PT-symmetric model. The large-N limit of this class of models exists, and properties of the lowest-lying singlet state can be computed using WKB. For $p=3,4$, the energy of this state for small values of $N$ appears to show rapid convergence to the large-N limit. For the special case of $p=4$, we extend recent work on the $-gx^{4}$ potential to the matrix model: we show that the PT-symmetric matrix model is equivalent to a hermitian matrix model with a potential proportional to $+(4g/N)TrΠ^{4}$. However, this hermitian equivalent model includes an anomaly term $\hbar\sqrt{2g/N}TrΠ$. In the large-N limit, the anomaly term does not contribute at leading order to the properties of singlet states.
dc.description6 pages, 1 table, no figures
dc.identifierhttps://arxiv.org/abs/hep-th/0701207
dc.identifierhttp://arxiv.org/abs/hep-th/0701207
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124187
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.titlePT-Symmetric Matrix Quantum Mechanics
dc.typetext

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