Clifford-like calculus over lattices
type: Item
instance of: scholarly article
title: Clifford-like calculus over lattices
zbMATH Open document ID: 0886.15036
DOI: 10.1007/BF03041215
author: Jayme Vaz
published in: Advances in Applied Clifford Algebras
publication date: 1997-11-25T00:00:00Z
review text: The author introduces a lattice generalization of Clifford algebras and the corresponding calculus. It is explicitly shown that, in contrast to the continuum case, Clifford algebras are not adequate for lattice problems. The new algebraic structure introduced (which reduces to the Clifford algebra structure in the continuum limit) solves all the problems and permits the development of a formalism analogous to the differential geometry of the continuum, also in the sense of having intrinsic expressions. The crucial aspect of the paper is the construction of the lattice Dirac operator. Several applications to lattice gauge theories, including the fermion doubling problem, are analyzed with detail in the new formalism. To sum up, this is a nice and creative paper on the subject, which must be studied by those interested in generalizations of the Clifford algebra structure.
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 15A90
zbMATH DE Number: 1091021
zbMATH Keywords: lattice generalization
zbMATH Keywords: Clifford algebras
zbMATH Keywords: differential geometry
zbMATH Keywords: lattice Dirac operator
zbMATH Keywords: lattice gauge theories
reviewed by: Waldyr A. jun. Rodrigues
MaRDI profile type: Publication
cites work: Q3994406
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full work available at URL: https://doi.org/10.1007/bf03041215
OpenAlex ID: W1963705150
description: scientific article; zbMATH DE number 1091021