and $j$ (as before) number the lattice points and $a_{i,\sigma }$ $%
(a_{i,\sigma }^{+})$ are the Hubbard operators, defined by (9).

Conclusions
===========

Using a new, nonperturbative approach, basing on the equivalent form of the Hubbard Hamiltonian, represented by the collection of interacting dimers (4) where each dimer problem has been exactly solved, we have expressed the annihilation (creation) operators (B.1)-(B.4) as linear combinations of transition operators between different dimer states (dimer representation). This method made it possible to exclude from the considerations the unoccupied dimer energy levels in the large $U$ limit by means of the projection technique resulting in the final Hamiltonian for the dimer itself (14), as well as, for the crystal as a whole (see (23), (24) and (C.6)). It is important to stress that the elimination of the unoccupied dimer energy levels was the only assumption to derive the Hubbard Hamiltonian (24) in the large $U$ limit. Therefore we can be sure that expanding (24) with respect to $x=\frac tU$ (Taylor expansion) we obtain absolutely all terms proportional to $x^n$ $(n=1,2,...).$ In other words all the coefficients proportional to $x^n$ are easy to control what is not always the case when using another methods. The 