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

TL;DR

This paper investigates a zero-dimensional PT-symmetric quartic theory, revealing its unique properties that differ from conventional theories, including evasion of the Mermin-Wagner-Coleman theorem and unusual Green's function limits.

Contribution

It provides a detailed analysis of PT-symmetric $ ext{φ}^4$ theory in zero dimensions, highlighting its distinct behavior from standard quartic theories.

Findings

Evasion of the Mermin-Wagner-Coleman theorem in PT-symmetric theory

Different results for Green's functions depending on the limit approach

Distinct properties compared to conventional quartic theories

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.