A discrete model of the Dirac-Kähler equation

Abstract

We construct a new discrete analog of the Dirac-Kähler equation in which some key geometric aspects of the continuum counterpart are captured. We describe a discrete Dirac-Kähler equation in the intrinsic notation as a set of difference equations and prove several statements about its decomposition into difference equations of Duffin type. We study an analog of gauge transformations for the massless discrete Dirac-Kähler equations.

19 pages; added references; to appear in Rept. Math. Phys

References in corpus (3)

• Field theory of massive and massless vector particles in the Duffin - Kemmer - Petiau formalism
• Lattice calculations on the spectrum of Dirac and Dirac-Kähler operators
• Dirac-Kahler Theory and Massless Fields

Cited by in corpus (11)

• A conformal group approach to the Dirac-Kähler system on the lattice
• On the chirality of a discrete Dirac-Kähler equation
• On fractional semidiscrete Dirac operators of Lévy-Leblond type
• Discrete Dirac-Kähler and Hestenes equations
• Time-changed Dirac-Fokker-Planck equations on the lattice
• A discrete Dirac-Kähler equation using a geometric discretisation scheme
• A discrete version of plane wave solutions of the Dirac equation in the Joyce form
• Discrete versions of some Dirac type equations and plane wave solutions
• On a semi-discrete model of Maxwell's equations in three and two dimensions
• Chiral properties of discrete Joyce and Hestenes equations
• 2D discrete Hodge-Dirac operator on the torus