类时轨迹

本书暂定概念：尚未进入正式概念库。下面是本书给出的定义原文。

定义 · 1.2 相对论粒子

相对论粒子的作用量有一个漂亮的几何解释：它使起点与终点在闵可夫斯基空间中的距离取极值。具有静止质量 m 的粒子沿一条类时轨迹(timelike trajectory)运动，该曲线上任意两点都满足 $d{s}^2<0$。因此我们取作用量为

$$\begin{array}{rl}& S=-mc{\int }_{x_{\mathrm{initial}}}^{x_{\mathrm{final}}}\sqrt{-d{s}^2}\\ & =-mc{\int }_{{\sigma }_1}^{{\sigma }_2}d\sigma \sqrt{-{\eta }_{\mu \nu }\frac{d{x}^{\mu }}{d\sigma }\frac{d{x}^{\nu }}{d\sigma }}\end{array}\text{\hspace{1em}(1.13)}$$

英文原文

The action for a relativistic particle has a nice geometric interpretation: it extremises the distance between the starting and end points in Minkowski space. A particle with rest mass m follows a timelike trajectory, for which any two points on the curve have $d{s}^2<0$ . We therefore take the action to be

$$\begin{array}{rl}& S=-mc{\int }_{x_{\mathrm{initial}}}^{x_{\mathrm{final}}}\sqrt{-d{s}^2}\\ & =-mc{\int }_{{\sigma }_1}^{{\sigma }_2}d\sigma \sqrt{-{\eta }_{\mu \nu }\frac{d{x}^{\mu }}{d\sigma }\frac{d{x}^{\nu }}{d\sigma }}\end{array}\text{\hspace{1em}(1.13)}$$

出处：1.2 相对论粒子 · node a-730f0f3d94703a8563122990 · 源节点 SHA-256 4fd65b3fa029aabc…