The consequences of non-normality

The non-normality of Wilson-type lattice Dirac operators has important consequences — the application of the usual concepts from the textbook (hermitian) quantum mechanics should be reconsidered. This includes an appropriate definition of observables and the refinement of computational tools. We show that the truncated singular value expansion is the optimal approximation to the inverse operator D−1 and we prove that due to the γ5-hermiticity it is equivalent to γ5 times the truncated eigenmode expansion of the hermitian Wilson-Dirac operator.