On the chirality of a discrete Dirac-Kähler equation

Abstract

We discuss a discrete analogue of the Dirac-Kähler equation in which chiral properties of the continual counterpart are captured. We pay special attention to a discrete Hodge star operator. To build one a combinatorial construction of double complex is used. We describe discrete exterior calculus operations on a double comlex and obtain the discrete Dirac-Kähler equation using these tools. Self-dual and anti-self-dual discrete inhomogeneous forms are presented. The chiral invariance of the massless discrete Dirac-Kähler equation is shown. Moreover, in the massive case we prove that a discrete Dirac-Kähler operator flips the chirality.

18 pages. arXiv admin note: substantial text overlap with arXiv:1307.1220

References in corpus (2)

• A discrete model of the Dirac-Kähler equation
• The chiral and flavour projection of Dirac-Kahler fermions in the geometric discretization

Cited by in corpus (5)

• Discrete Dirac-Kähler and Hestenes equations
• 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
• Chiral properties of discrete Joyce and Hestenes equations