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A new construction for spinor wave equations

机译:旋波方程的新构造

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摘要

The construction of discrete scalar wave propagation equations in arbitrary inhomogeneous media was recently achieved by using elementary dynamical processes realizing a discrete counterpart of the Huygens principle. In this paper, we generalize this approach to spinor wave propagation. Although the construction can be formulated on a discrete lattice of any dimension, for simplicity we focus on spinors living in 1 + 1 space-time dimensions. The Dirac equation in the Majorana-Weyl representation is directly recovered by incorporating appropriate symmetries of the elementary processes. The Dirac equation in the standard representation is also obtained by using its relationship with the Majorana-Weyl representation.
机译:最近,通过使用基本动力学过程实现了惠更斯原理的离散对应物,在任意不均匀介质中构造了离散标量波传播方程。在本文中,我们将这种方法推广到自旋波传播。尽管可以将结构构造为任意尺寸的离散晶格,但为简单起见,我们将重点放在生活在1 +1时空尺寸中的棘突上。通过合并基本过程的适当对称性,直接恢复马约拉纳-魏尔表示中的狄拉克方程。标准表示中的狄拉克方程也可以通过使用与马约拉纳-韦尔表示的关系来获得。

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