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arXiv · 0707.1655

PT-symmetric Models with O(N) Symmetry

Peter N. Meisinger·Michael C. Ogilvie
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Abstract

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 $-g(\vecϕ^{2})^{2}/N$ PT-symmetric scalar field theories are asymptotically free.

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Peter N. Meisinger, Michael C. Ogilvie. 2007-07-11. PT-symmetric Models with O(N) Symmetry. https://arxiv.org/abs/0707.1655

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