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arXiv · 1411.7673

On the chirality of a discrete Dirac-K\"ahler equation

Volodymyr Sushch
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Abstract

We discuss a discrete analogue of the Dirac-K\"{a}hler 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-K\"{a}hler equation using these tools. Self-dual and anti-self-dual discrete inhomogeneous forms are presented. The chiral invariance of the massless discrete Dirac-K\"{a}hler equation is shown. Moreover, in the massive case we prove that a discrete Dirac-K\"{a}hler operator flips the chirality.

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Volodymyr Sushch. 2014-11-27. On the chirality of a discrete Dirac-K\"ahler equation. https://doi.org/10.1016/s0034-4877(15)30028-8

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