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

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.