2007/07/11 by Peter N. Meisinger, Meisinger, Peter N., Michael C. Ogilvie +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.0707.1655
8 pages, no figures
arxiv created 2007/07/11 · arxiv updated 2009/12/01
We construct PT-symmetric quantum mechanical models with an O(N)-symmetric interaction term of the form -g(x2)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(ϕ2)2/N PT-symmetric scalar field theories are asymptotically free.