An approximation scheme determining the excitations of crystalline solids is proposed. It relies on "downfolding" of the original microscopic model to a simpler low energy electronic model on the lattice with pairwise interactions. A truncation of the set of Dyson - Schwinger equations of the low energy model, supplemented by a systematic "covariant" calculation of correlators lead to a converging series of approximates. The covariance ensures all the Ward identities among correlators describing various condensed matter probes. It is shown that the third order approximant of this kind (beyond classical and gaussian (Hartree - Fock) is precise enough and due to several fortunate features the complexity of calculation is surprisingly low so that a realistic material computation is feasible. The scheme was tested on several solvable benchmark models.

Prof. Baruch Rosenstein (Ph. D. from Tel Aviv University, Israel in 1987) started his research carrier in field theory. However after postdoc in UT Austin with S. Weinberg switched to condensed matter theory. In UBC (Vancouver) developed the Kosterlitz –Thouless phase transition theory of 2D superconductors and theory of 2D systems of interacting Dirac quasi-particles (nowadays exemplified by graphene). The work resulted in a description of the chiral phase transitions (Phys. Rep., 1992). During next 15 years worked mainly on the vortex physics in high Tc superconductors (summarized in Rev. Mod. Phys. 2010 review and textbook/monograph in press). Since 1996 taught at Taiwan Chiao Tung University.