The pseudodiffential pertubations of the Dirac operator and the Kastler-Kalau-Walze type theorems

In [7], Kastler gave a brute-force proof of the fact, announced by Connes,that the Wodzicki residue of the inverse square of the Dirac operator D isproportional to the Einstein-Hilbert action of general relativity. In thispaper, we obtain the Wodzicki residue of the inverse square of thepseudodiffential pertubations of the Dirac operator. And we give the proof ofthe Kastler-Kalau-Walze type theorems for the pseudodiffential pertubations ofthe Dirac operator on 4-dimensional compact manifolds with boundary.