Advances in Applied Clifford Algebras

, Volume 7, Issue 1, pp 37–70 | Cite as

Clifford-like calculus over lattices



We introduce a calculus over a lattice based on a lattice generalization of the Clifford algebras. We show that Clifford algebras, in contrast to the continuum, are not an adequated algebraic structure for lattice problems. Then we introduce a new algebraic structure, that reduces to a Clifford algebra in the continuum limit, in terms of which we can develop a formalism analogous to the differential geometry of the continuum, also in the sense that we have intrinsic expressions. The differential operator is given by the graded commutator of an operator that generalizes the Dirac operator. We also discuss the applications of this formalism in lattice gauge theories, with particular attention to the fermion doubling problem.


Dirac Operator Differential Form Lattice Version Clifford Algebra Lattice Gauge Theory 
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Copyright information

© Birkhäuser-Verlag AG 1997

Authors and Affiliations

  1. 1.Department of PhysicsSyracuse UniversitySyracuseUSA

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