# A discrete model of the Dirac-Kähler equation

@article{Sushch2014ADM, title={A discrete model of the Dirac-K{\"a}hler equation}, author={Volodymyr Sushch}, journal={Reports on Mathematical Physics}, year={2014}, volume={73}, pages={109-125} }

We construct a new discrete analogue of the Dirac–Kahler equation in which some key geometric aspects of the continuum counterpart are captured. We describe a discrete Dirac–Kahler equation in the intrinsic notation as a set of difference equations and prove several statements about its decomposition into difference equations of Duffin type. We study an analogue of gauge transformations for the massless discrete Dirac–Kahler equations.

## 11 Citations

Discrete Dirac-Kähler equation and its formulation in algebraic form

- Mathematics, Physics
- 2016

A relationship between the discrete Dirac-Kahler equation and discrete analogues of some Dirac type equations in the geometric spacetime algebra is discussed. We show that a solution of the discrete…

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

- Mathematics, Physics
- 2014

We discuss a discrete analogue of the Dirac-Kahler equation in which chiral properties of the continual counterpart are captured. We pay special attention to a discrete Hodge star operator. To build…

A Discrete Dirac–Kähler Equation Using a Geometric Discretisation Scheme

- Mathematics, PhysicsAdvances in Applied Clifford Algebras
- 2018

Discrete models of the Dirac–Kähler equation and the Dirac equation in the Hestenes form are discussed. A discrete version of the plane wave solutions to a discrete analogue of the Hestenes equation…

A Discrete Version of Plane Wave Solutions of the Dirac Equation in the Joyce Form

- Mathematics, Physics
- 2019

We construct a discrete version of the plane wave solution to a discrete Dirac-Kähler equation in the Joyce form. A geometric discretisation scheme based on both forward and backward difference…

Discrete versions of some Dirac type equations and plane wave solutions

- Mathematics, Physics
- 2017

A discrete version of the plane wave solution to some discrete Dirac type equations in the spacetime algebra is established. The conditions under which a discrete analogue of the plane wave solution…

A conformal group approach to the Dirac–Kähler system on the lattice

- Mathematics, Physics
- 2016

Starting from the representation of the (n − 1) + n − dimensional Lorentz pseudo-sphere on the projective space PRn,n, we propose a method to derive a class of solutions underlying to a Dirac–Kahler…

Discrete Dirac-K\"ahler and Hestenes equations

- Mathematics, Physics
- 2015

A discrete analogue of the Dirac equation in the Hestenes form is constructed by introduction the Clifford product on the space of discrete forms. We discuss the relation between the discrete…

DKP algebra, DKP equation, and differential forms

- MathematicsJournal of Mathematical Physics
- 2018

It is well known that the Clifford algebras and the Dirac equation have a representation in terms of differential forms known as the Kahler-Atiyah algebra and the Dirac-Kahler equation, respectively.…

On fractional semidiscrete Dirac operators of L\'evy-Leblond type

- Mathematics
- 2021

In this paper we introduce a wide class of space-fractional and time-fractional fractional semidiscrete Dirac operators of Lévy-Leblond type on the semidiscrete space-time hZ × [0,∞) (h > 0),…

Chiral Properties of Discrete Joyce and Hestenes Equations

- Physics, Mathematics
- 2019

This paper concerns the question of how chirality is realized for discrete counterparts of the Dirac-K\"{a}hler equation in the Hestenes and Joyce forms. It is shown that left and right chiral states…

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