PTsymmetry and large-Nmodels

DOI10.1088/1751-8113/41/24/244021zbMATH Open1140.81364arXiv0804.0778OpenAlexW3124939486MaRDI QIDQ3509607

Michael C. Ogilvie, Peter N. Meisinger

Publication date: 2 July 2008

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Abstract: Recently developed methods for PT-symmetric models can be applied to quantum-mechanical matrix and vector models. In matrix models, the calculation of all singlet wave functions can be reduced to the solution a one-dimensional PT-symmetric model. The large-N limit of a wide class of matrix models exists, and properties of the lowest-lying singlet state can be computed using WKB. For models with cubic and quartic interactions, the ground state energy appears to show rapid convergence to the large-N limit. For the special case of a quartic model, we find explicitly an isospectral Hermitian matrix model. The Hermitian form for a vector model with O(N) symmetry can also be found, and shows many unusual features. The effective potential obtained in the large-N limit of the Hermitian form is shown to be identical to the form obtained from the original PT-symmetric model using familiar constraint field methods. The analogous constraint field prescription in four dimensions suggests that PT-symmetric scalar field theories are asymptotically free.

Full work available at URL: https://arxiv.org/abs/0804.0778

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)