On the Chirality of a Discrete Dirac–Kähler Equation. Issue 2 (October 2015)

• Record Type: Journal Article
• Authors: Sushch, Volodymyr
• Is Part Of: Reports on mathematical physics. Volume 76:Issue 2(2015)
• Page Start: 179
• Page End: 196
• Publication Date: 2015-10
• Subjects: Dirac–Kähler equation -- chirality -- Hodge star operator -- difference equations -- discrete models; Mathematical physics -- Periodicals; Physique mathématique -- Périodiques; 530.15
• DOI: 10.1016/S0034-4877(15)30028-8
• Languages: English
• ISSNs: 0034-4877

Abstract

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.