Chiral fermion operators on the lattice

Details Chiral fermion operators on the lattice Chiral fermion operators on the lattice

2002-12-13

arxiv.org/abs/hep-lat/0212021v1

Int.J.Mod.Phys. A18 (2003) 2565-2590

Physics

High Energy Physics

High Energy Physics - Lattice

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

Scientific paper

10.1142/S0217751X03013910

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 r\^ole 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.

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