自旋进动关于参考同余的协变形式
A covariant formalism of spin precession with respect to a reference congruence
摘要：
我们导出了一个有效的三维相对论自旋进动形式。形式主义是适用于任何时空中的任意类时参考世界线同余是指定的。我们使用了一个被停止的自旋向量，这个自旋向量是，如果我们对自旋向量做一个简单的提升，使它相对于同余停止，就会得到的。从标准自旋矢量的费米输运方程出发，导出了相应的停止自旋矢量的输运方程。利用一个矢量沿世界线的时空输运方程，对应于关于同余的空间平行输运，我们可以写出陀螺仪相对于由同余定义的局部空间几何的进动公式。这种一般方法已经被Jantzen et.（参见例如Jantzen，Carini和Bini，Ann.Phys.215（1997）1），但是我们各自表达式的代数形式不同。我们也适用于形式主义的一种新型的空间并行传输介绍琼森（类。量子重力23（2006）1），以及验证即将发表的论文（Jonsson，Am.你好75（2007）463），其中陀螺仪进动完全被解释为双托马斯型效应。我们还提出了明确的三维形式（使用黑体矢量符号）的形式主义，并给出应用程序的例子。
英文摘要：
We derive an effectively three-dimensional relativistic spin precession formalism. The formalism is applicable to any spacetime where an arbitrary timelike reference congruence of worldlines is specified. We employ what we call a stopped spin vector which is the spin vector that we would get if we momentarily make a pure boost of the spin vector to stop it relative to the congruence. Starting from the Fermi transport equation for the standard spin vector we derive a corresponding transport equation for the stopped spin vector. Employing a spacetime transport equation for a vector along a worldline, corresponding to spatial parallel transport with respect to the congruence, we can write down a precession formula for a gyroscope relative to the local spatial geometry defined by the congruence. This general approach has already been pursued by Jantzen et. al. (see e.g. Jantzen, Carini and Bini, Ann. Phys. 215 (1997) 1), but the algebraic form of our respective expressions differ. We are also applying the formalism to a novel type of spatial parallel transport introduced in Jonsson (Class. Quantum Grav. 23 (2006) 1), as well as verifying the validity of the intuitive approach of a forthcoming paper (Jonsson, Am. Journ. Phys. 75 (2007) 463) where gyroscope precession is explained entirely as a double Thomas type of effect. We also present the resulting formalism in explicit three-dimensional form (using the boldface vector notation), and give examples of applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
