2007/01/23 by Peter N. Meisinger, Meisinger, Peter N., Michael C. Ogilvie +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.hep-th/0701207
6 pages, 1 table, no figures
arxiv created 2007/01/23 · openalex publication_date 2007/01/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently 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/Np/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 -gx4 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)TrΠ4. However, this hermitian equivalent model includes an anomaly term ℏ√(2g/N)TrΠ. In the large-N limit, the anomaly term does not contribute at leading order to the properties of singlet states.