To make the field-theoretic methodology amenable for computation, Baeurle proposed to shift the contour of integration of the partition function integral through the homogeneous mean field (MF) solution using Cauchy's integral theorem, which provides its so-called mean-field representation. This strategy was previously successfully employed in field-theoretic electronic structure calculations (Rom 1997, Baer 1998). Baeurle could demonstrate that this technique provides a significant acceleration of the statistical convergence of the ensemble averages in the MC sampling procedure (Baeurle 2002).