Solutions for the Klein-Gordon and Dirac equations on the lattice based on Chebyshev polynomials

Abstract

The main goal of this paper is to adopt a multivector calculus scheme to study finite difference discretizations of Klein-Gordon and Dirac equations for which Chebyshev polynomials of the first kind may be used to represent a set of solutions. The development of a well-adapted discrete Clifford calculus framework based on spinor fields allows us to represent, using solely projection based arguments, the solutions for the discretized Dirac equations from the knowledge of the solutions of the discretized Klein-Gordon equation. Implications of those findings on the interpretation of the lattice fermion doubling problem is briefly discussed.

20 pages; accepted for publication at Complex Analysis and Operator Theory (CAOT)

References in corpus (3)

• Creutz Fermions on an Orthogonal Lattice
• Fock Spaces, Landau Operators and the Regular Solutions of time-harmonic Maxwell equations
• Classes of hypercomplex polynomials of discrete variable based on the quasi-monomiality principle

Cited by in corpus (8)

• A conformal group approach to the Dirac-Kähler system on the lattice
• On fractional semidiscrete Dirac operators of Lévy-Leblond type
• Relativistic Wave Equations on the lattice: an operational perspective
• Time-changed Dirac-Fokker-Planck equations on the lattice
• A note on the discrete Cauchy-Kovalevskaya extension
• A discrete Dirac-Kähler equation using a geometric discretisation scheme
• A discrete version of plane wave solutions of the Dirac equation in the Joyce form
• Chiral properties of discrete Joyce and Hestenes equations