Algebraic derivation of symmetry relations for disordered electronic systems

Abstract

By means of “superfields” two time-reversal invariant disordered electronicn-orbital models one without, the other with a spin-dependent random potential can be described by the same Lagrangian except for the sign of an overall prefactor. Similarly two different treatments of a system which breaks time-reversal invariance yields the same Lagrangian but with opposite sign of the prefactor. Since this prefactor is proportional ton, identical saddle point expansions in powers of ±n ⁻¹ for the averaged Green's functions are obtained, relations first found diagrammatically by Oppermann and Jüngling. The invariance of the Lagrangian under unitary graded and unitary orthosymplectic transformations of the fields for systems without and with time-reversal invariance, respectively, is pointed out.