Causal wave propagation for relativistic massive particles: physical asymptotics in action
Causal wave propagation for relativistic massive particles: physical asymptotics in action
复制标题
相对论大质量粒子的因果波传播：物理渐进的作用
DOI：
--
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
M. Berry
中科院分区：
文献类型：
--
作者：
M. Berry
波包表示从一个在确定时间开启的源注入半空间的相对论量子粒子，由必须包含负频率的平面波的叠加表示。传播是因果关系：解析性的结果是，在时间t，波的任何部分都没有传播得比对应于信号的前沿的CT更远。然而，前面后面的干涉条纹是以超光速传播的。对于Klein-Gordon和Dirac波包，空间积分密度增加，因为在边界处注入电流。即使在最简单的因果模型中，理解长时间后的波的形状也是积分渐近性的有益练习，说明了适合研究生水平的几种技术;不同的空间特征涉及来自极点和来自两个鞍点的贡献，接近鞍点的极点的一致渐近性，以及两个鞍状物的结合，形成了紧挨在前面的索末菲前体。
Wavepackets representing relativistic quantum particles injected into a half-space, from a source that is switched on at a definite time, are represented by superpositions of plane waves that must include negative frequencies. Propagation is causal: it is a consequence of analyticity that at time t no part of the wave has travelled farther than ct, corresponding to the front of the signal. Nevertheless, interference fringes behind the front travel superluminally. For Klein–Gordon and Dirac wavepackets, the spatially integrated density increases because current is injected at the boundary. Even in the simplest causal model, understanding the shape of the wave after long times is an instructive exercise in the asymptotics of integrals, illustrating several techniques at a level suitable for graduate students; different spatial features involve contributions from a pole and from two saddle points, the uniform asymptotics for the pole close to a saddle, and the coalescence of two saddles into the Sommerfeld precursor immediately behind the front.