On the Chirality of a Discrete Dirac–Kähler Equation. Issue 2 (October 2015) - Sushch, Volodymyr
Abstract : We discuss a discrete analogue of the Dirac–Kähler equation in which chiral properties of the continuum counterpart are captured. We pay special attention to a discrete Hodge star operator. To build such an operator combinatorial construction of a double complex is used. We describe discrete exterior calculus operations on a double complex 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.