Clifford-like calculus over lattices
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.
scientific article; zbMATH DE number 1091021