## 17 Citations

### Discrete Dirac-Kähler equation and its formulation in algebraic form

- Mathematics
- 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…

### A Discrete Dirac–Kähler Equation Using a Geometric Discretisation Scheme

- MathematicsAdvances 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 Dirac–Kähler Equation Using a Geometric Discretisation Scheme

- MathematicsAdvances 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

- MathematicsAdvances in Applied Clifford Algebras
- 2020

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…

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

- Mathematics
- 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…

### 2D discrete Hodge-Dirac operator on the torus

- Mathematics, Computer ScienceSymmetry
- 2022

The goal of this work is to develop a satisfactory discrete model of the de Rham–Hodge theory on manifolds that are homeomorphic to the torus that is compatible with the Hodge decomposition theorem.

### Discrete versions of some Dirac type equations and plane wave solutions

- Mathematics
- 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
- 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…

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

- Mathematics
- 2017

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–Kähler…

## References

SHOWING 1-10 OF 28 REFERENCES

### The Dirac-Kähler equation and fermions on the lattice

- Physics
- 1982

The geometrical description of spinor fields by E. Kähler is used to formulate a consistent lattice approximation of fermions. The relation to free simple Dirac fields as well as to Susskind's…

### Discrete model of Yang-Mills equations in Minkowski space

- Mathematics, Physics
- 2004

Using methods of differential geometry, a discrete analog of the Yang-Mills equations in Minkowski space is constructed. The gauge transformation law in a discrete formulation is given and gauge…

### Dirac‐Kähler Theory and Massless Fields

- Physics, Mathematics
- 2010

Three massless limits of the Dirac‐Kahler theory are considered. It is shown that the Dirac‐Kahler equation for massive particles can be represented as a result of the gauge‐invariant mixture…

### Note on Dirac–Kähler massless fields

- Physics
- 2009

We obtain the canonical and symmetrical Belinfante energy-momentum tensors of Dirac–Kähler’s fields. It is shown that the traces of the energy-momentum tensors are not equal to zero. We find the…

### DIRAC–KÄHLER FERMION FROM CLIFFORD PRODUCT WITH NONCOMMUTATIVE DIFFERENTIAL FORM ON A LATTICE

- Physics, Mathematics
- 2004

We formulate Dirac–Kahler fermion action by introducing a new Clifford product with noncommutative differential form on a lattice. Hermiticity of the Dirac–Kahler action requires to choose the…

### Decomposition of the Kähler equation

- Mathematics
- 1996

It is shown that the Kähler equation in a four-dimensional pseudo-Riemannian manifold with Lorentzian signature decomposes uniquely into four uncoupled equations of Duffin type.

### Lattice calculations on the spectrum of Dirac and Dirac-Kähler operators

- Mathematics, Physics
- 2008

We use a lattice formulation to study the spectra of the Dirac and the Dirac–Kahler operators on the 2-sphere. This lattice formulation uses differentiation matrices which yield exact values for the…

### Lattice electromagnetic theory from a topological viewpoint

- Mathematics
- 1999

The language of differential forms and topological concepts are applied to study classical electromagnetic theory on a lattice. It is shown that differential forms and their discrete counterparts…

### Dirac-Kähler fermions and exact lattice supersymmetry

- Physics
- 2005

We discuss a new approach to putting supersymmetric theories on the lattice. The basic idea is to start from a twisted formulation of the underlying supersymmetric theory in which the fermions are…