Chiral fermion operators on the lattice

Abstract

We only require generalized chiral symmetry and ${\gamma }_5$-hermiticity, which leads to a large class of Dirac operators describing massless fermions on the lattice, and use this framework to give an overview of developments in this field. Spectral representations turn out to be a powerful tool for obtaining detailed properties of the operators and a general construction of them. A basic unitary operator is seen to play a central rôle in this context. We discuss a number of special cases of the operators and elaborate on various aspects of index relations. We also show that our weaker conditions lead still properly to Weyl fermions and to chiral gauge theories.

25 pages, invited review article for Int. J. Mod. Phys. A

References in corpus (12)

• Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
• The index theorem in QCD with a finite cut-off
• Testing the fixed-point QCD action and the construction of chiral currents
• Topological Charge and The Spectrum of Exactly Massless Fermions on the Lattice
• Algebraic Generalization of the Ginsparg-Wilson Relation
• Ginsparg-Wilson operators and a no-go theorem
• The Index of a Ginsparg-Wilson Dirac operator
• Chiral Anomaly for a New Class of Lattice Dirac Operators
• More chiral operators on the lattice
• Chiral fermions on the lattice and index relations
• General Ginsparg-Wilson fermions and index
• Differential equation for spectral flows of hermitean Wilson-Dirac operator

Cited by in corpus (2)

• New solutions to the Ginsparg-Wilson equation
• The Auxiliary Field Method in Quantum Mechanical Four-Fermi Models -- A Study Toward Chiral Condensation in QED