Chiral fermions on the lattice and index relations

Abstract

Comparing recent lattice results on chiral fermions and old continuum results for the index puzzling questions arise. To clarify this issue we start with a critical reconsideration of the results on finite lattices. We then work out various aspects of the continuum limit. After determining bounds and norm convergences we obtain the limit of the anomaly term. Collecting our results the index relation of the quantized theory gets established. We then compare in detail with the Atiyah-Singer theorem. Finally we analyze conventional continuum approaches.

34 pages; a more detaild introduction and a subsection with remarks on literature added

References in corpus (6)

• Bounds on the Wilson Dirac Operator
• Algebraic Generalization of the Ginsparg-Wilson Relation
• Relation $Tr{\gamma }_5=0$ and the index theorem in lattice gauge theory
• Differential equation for spectral flows of hermitean Wilson-Dirac operator
• General Ginsparg-Wilson fermions and index
• Dirac operator index and topology of lattice gauge fields

Cited by in corpus (4)

• More chiral operators on the lattice
• Effect of r averaging on Chiral Anomaly in Lattice QCD with Wilson Fermion: Finite volume and cutoff effects
• General chiral gauge theories on the lattice
• Chiral fermion operators on the lattice