A New Fermion Many-Body Theory Based on the SO(2N+1) Lie Algebra of the Fermion Operators

A new many-body theory for fermions is proposed wihich is based on the SO(2N+1) Lie algebra of the fermion operators consisted of the annihilation-creation operators and the pair operators. A New cannonical transformation, which is the extension of the Bogoliubov transformation to the SO(2N+1) group, is introduced. A new bose representation for the fermion Lie operators is obtained by mapping the fermion Lie operators into the regular representation of the SO(2N+1) group. The annihilation-creation operators and the pair operators of fermions are represented by the closed first order differential operators on the SO(2N+1) group. An exact representation of fermion wavefunctions in a form similar to the wavefunction of the generator coordinate method is obtained making use of the SO(2N+1) canonical transformation. The physical fermion space is shown to be the irreducible spinor representation of the SO(2N+1) group. The dynamics of fermions in the bose representation space is shown to represent rotations of a 2N+1 dimensional rotator.