Quantum field theory for electrons and holes in planar systems and currents obtained by electrons-holes pairs in high-TC materials
Quantum field-theory-equations based on SO(2,1) group are suggested for treating electrons and holes in planar systems. Non-unitary representations are developed and their properties are related to pseudo-Hermitian metrics. These equations can be used for treating holes-electron pairing in high TC materials where in a non-relativistic approximation we exchange the relativistic energy gap into the relatively small energy band gap. It is shown that while holes or electrons satisfy separately Pauli-exclusion principle, with anti-commutation relations, the holes-electron pairs follow bosonic commutation relations. Bose-Einstein distribution for excitons in planar systems is calculated. The conditions under which the excitons have small momenta, and many excitons are included within an are of exciton wavelength dimensions, are analyzed. The physical implications of these properties to high TC currents in planar systems are discussed.