PT-symmetric Models with O(N) Symmetry

Details PT-symmetric Models with O(N) Symmetry PT-symmetric Models with O(N) Symmetry

2007-07-11

arxiv.org/abs/0707.1655v1

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, no figures

Scientific paper

We construct PT-symmetric quantum mechanical models with an O(N)-symmetric interaction term of the form $-g(\vec{x}^{2})^{2}/N$. Using functional integral methods, we find the equivalent Hermitian model, which has several 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 $-g(\vec{\phi}^{2})^{2}/N$ PT-symmetric scalar field theories are asymptotically free.

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