Solutions for the Klein–Gordon and Dirac Equations on the Lattice Based on Chebyshev Polynomials

被引：0
作者：
Nelson Faustino
机构：
[1] Estatística e Computação Científica Universidade Estadual de Campinas,Departamento de Matematica Aplicada, Instituto de Matemática
来源：
Complex Analysis and Operator Theory | 2016年 / 10卷
关键词：
Chebyshev polynomials; Discrete Dirac operators; Lattice fermion doubling; Spinor fields; Primary 30G35; 39A12; Secondary 33C05; 53Z05;
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学科分类号：
摘要：
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.
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页码：379 / 399
页数：20
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