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arXiv · 1501.00514

PT-symmetric $\varphi^4$ theory in d=0 dimensions

Carl M. Bender·Vincenzo Branchina·Emanuele Messina
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Abstract

A detailed study of a PT-symmetric zero-dimensional quartic theory is presented and a comparison between the properties of this theory and those of a conventional quartic theory is given. It is shown that the PT-symmetric quartic theory evades the consequences of the Mermin-Wagner-Coleman theorem regarding the absence of symmetry breaking in d<2 dimensions. Furthermore, the PT-symmetric theory does not satisfy the usual Bogoliubov limit for the construction of the Green's functions because one obtains different results for the $h\to0^-$ and the $h\to0^+$ limits.

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Carl M. Bender, Vincenzo Branchina, Emanuele Messina. 2015-01-02. PT-symmetric $\varphi^4$ theory in d=0 dimensions. https://arxiv.org/abs/1501.00514

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