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 D…
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