The Consequences of Non-Normality

Abstract

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 gamma_5-hermiticity it is equivalent to gamma_5 times the truncated eigenmode expansion of the hermitian Wilson-Dirac operator.

Lattice2001(theorydevelop)

References in corpus (1)

• Non-Hermitian Delocalization and Eigenfunctions

Cited by in corpus (4)

• Acceleration of the Arnoldi method and real eigenvalues of the non-Hermitian Wilson-Dirac operator
• Spectral properties and chiral symmetry violations of (staggered) domain wall fermions in the Schwinger model
• Index theorem with Minimally Doubled Fermions in four space-time dimensions
• Topological properties of minimally doubled fermions in two space-time dimensions