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The spectral theorem of many-body Green's function theory relatesthermodynamic correlations to Green's functions. More often than not, thematrix governing the equations of motion has zero eigenvalues. In this case,the standard text-book approach requires both commutator and anti-commutatorGreen's functions to obtain equations for that part of the correlation whichdoes not lie in the null space of the matrix. In this paper, we show that thisprocedure fails if the projector onto the null space is dependent on themomentum vector. We propose an alternative formulation of the theory in termsof the non-null space alone and we show that a solution is possible if one canfind a momentum-independent projector onto some subspace of the non-null space.To do this, we enlist the aid of the singular value decomposition (SVD) of theequation of motion matrix in order to project out the null space, thus reducingthe size of the matrix and eliminating the need for the anti-commutator Green'sfunction. We extend our previous work, dealing with a ferromagnetic Heisenbergmonolayer and a momentum-independent projector onto the null space, where bothmultilayer films and a momentum-dependent projector are considered. We developthe numerical methods capable of handling these cases and offer a computationalalgorithmus that should be applicable to any similar problem arising in Green'sfunction theory.Comment: 16 pages, 7 figure

The treatment of zero eigenvalues of the matrix governing the equations of motion in many-body Green function theory