Article ID Journal Published Year Pages File Type
1899218 Reports on Mathematical Physics 2015 18 Pages PDF
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.
Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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