The Dirac Operator over Abelian Finite Groups

Details The Dirac Operator over Abelian Finite Groups The Dirac Operator over Abelian Finite Groups

1997-06-26

arxiv.org/abs/hep-th/9706189v1

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, LaTeX 2e, amsmath and amssymb packages

Scientific paper

In this paper we show how to construct a Dirac operator on a lattice in complete analogy with the continuum. In fact we consider a more general problem, that is, the Dirac operator over an abelian finite group (for which a lattice is a particular example). Our results appear to be in direct connexion with the so called fermion doubling problem. In order to find this Dirac operator we need to introduce an algebraic structure (that generalizes the Clifford algebras) where we have quantities that work as square-root of the translation operator. Quantities like these square-roots have been used recently in order to provide an approach to fermions on the lattice that is free from doubling and has chiral invariance in the massless limit, and our studies seem to give a mathematical basis to it.

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