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A variation of Dirac equation based on SO(2,1) group is suggested fortreating low dimensional systems in the three dimensional x,y,t space.Non-unitary representations are developed in an analogous way to those used inthe ordinary Dirac equations and quantum field theory is developed for thepresent SO(2,1) relativistic equation. The theory is applied for lowdimensional systems including especially holes-electrons pairs, or othertwo-particle states, in the low dimensional space.

A Variation of Dirac Equation, Based on SO(2,1) Group, with Applications to Low Dimensional Systems