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

@article{Sushch2014OnTC,
  title={On the chirality of a discrete Dirac-K\"ahler equation},
  author={Volodymyr Sushch},
  journal={arXiv: Mathematical Physics},
  year={2014}
}
  • Volodymyr Sushch
  • Published 27 November 2014
  • Mathematics, Physics
  • arXiv: Mathematical Physics
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 one a combinatorial construction of double complex is used. We describe discrete exterior calculus operations on a double comlex and obtain the discrete Dirac-Kahler equation using these tools. Self-dual and anti-self-dual discrete inhomogeneous forms are presented. The chiral invariance of the… Expand
Discrete Dirac-Kähler equation and its formulation in algebraic form
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 discreteExpand
Discrete Dirac-K\"ahler and Hestenes equations
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 discreteExpand
A Discrete Dirac–Kähler Equation Using a Geometric Discretisation Scheme
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 equationExpand
A Discrete Version of Plane Wave Solutions of the Dirac Equation in the Joyce Form
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 differenceExpand
Discrete versions of some Dirac type equations and plane wave solutions
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 solutionExpand
Chiral Properties of Discrete Joyce and Hestenes Equations
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 statesExpand

References

SHOWING 1-10 OF 34 REFERENCES
A discrete model of the Dirac-Kähler equation
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 theExpand
The chiral and flavour projection of Dirac-Kahler fermions in the geometric discretization
It is shown that an exact chiral symmetry can be described for Dirac-Kahler fermions using the two complexes of the geometric discretization. This principle is extended to describe exact flavourExpand
Symplectic Dirac-K\"ahler Fields
For the description of space-time fermions, Dirac-K\"ahler fields (inhomogeneous differential forms) provide an interesting alternative to the Dirac spinor fields. In this paper we develop a similarExpand
The Dirac-Kähler equation and fermions on the lattice
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'sExpand
DIRAC–KÄHLER FERMION FROM CLIFFORD PRODUCT WITH NONCOMMUTATIVE DIFFERENTIAL FORM ON A LATTICE
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 theExpand
Dirac-Kähler fermions and exact lattice supersymmetry
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 areExpand
Chiral Dirac Fermions on the Lattice using Geometric Discretisation
Abstract A new approach to the problem of doubling [1] is presented with the Dirac-Kahler (DK) theory as a starting point and using Geometric Discretisation [2] providing us with a new way ofExpand
Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
Abstract It is shown that the Ginsparg-Wilson relation implies an exact symmetry of the fermion action, which may be regarded as a lattice form of an infinitesimal chiral rotation. Using this resultExpand
A Method for simulating chiral fermions on the lattice
Abstract I show that a lattice theory of massive interacting fermions in 2 n +1 dimensions may be used to simulate the behavior of massless chiral fermions in 2 n dimensions if the fermion mass has aExpand
Absence of neutrinos on a lattice: (I). Proof by homotopy theory
Abstract It is shown, by a homotopy theory argument, that for a general class of fermion theories on a Kogut-Susskind lattice an equal number of species (types) of left- and right-handed WeylExpand
...
1
2
3
4
...