The calculation of Green functions is a difficult though still
feasible task which belongs to the main constructive tools in the
relativistic quantum field theory. The paper pays attention to the
wrong-sign (i.e., manifestly non-Hermitian) quartic-interaction toy
model. The author makes use of the exceptional reducibility (i.e.,
Dyson's mapping) of this model to a Hermitian one, and he then
brings quantitative methods-comparing arguments which persuasively
support the preferability of the universal calculation method based
on the lowest-order truncation of the underlying Schwinger-Dyson
equations, with a key merit of circumventing the necessity of the
construction of the metric. This toy-model test seems to predict
good chances for the success of future calculations in higher orders
and/or in higher dimensions, where the use of other methods would
become prohibitively difficult.

MR2780948 Jones, H. F. Green functions for the wrong-sign quartic.
Internat. J. Theoret. Phys. 50 (2011), no. 4, 1071--1080. 81Qxx