On the Bosonization of the Many Electron Problem

The Garbaczewski bosonization procedure is applied to the many-electron problem. It leads to a non-local c-number path integral representation for the trace of the evolution operator which also depends on a mapping of the lattice points in the natural numbers. This mapping is needed for the implementation of the bosonization. We argue that the non-local interactions and the dependence on the mapping can be disregarded in the limit of small electron c-number field. We can then discuss the physics of the saddle point contribution. In the discussion the effects of the Pauli exclusion principle are introduced phenomenologically.