Charge transfer and the statistics of holons in a periodical lattice

The collective charge state (holon) in a periodical lattice is defined. The exact commutation relations for the holon operators correspond to the modi fied para-Fermi statistics of rank M (M is the number of lattice sites at w hich the hole can be created), i.e. one state can be occupied by up to M ho lons. At small concentration, the holon gas can be treated as a bosonic sys tem. In the general case, the holon gas is characterized by the immanent in teraction and coupling among the different holon band states, even in the a bsence of dynamic interactions (the so-called kinematic interaction). In sp ite of the kinematic interaction, there is no statistical prohibition of Bo se-Einstein condensation in the holon system. The possible extension of the approach developed to the coupled hole pairs in high-T-c superconductors i s discussed.