旋量波函数的基本动力学方程。I. Levy-Leblond和Schrodinger方程
Fundamental dynamical equations for spinor wave functions. I. Levy-Leblond and Schrodinger equations
摘要：
本文在伽利略时空中寻找二分量和四分量旋量波函数的基本（伽利略不变量）动力学方程。如果一个动力学方程在伽利略度规群的对称算符下是不变的，并且它的态函数像度规群的不可约表示那样变换，则它被认为是基本的。结果表明，不存在二分量旋量波函数的伽利略不变方程。本文给出了一种推导四分量旋量波函数的Lévy-Leblond方程的方法。形式上证明了Lévy-Leblond方程和薛定谔方程是唯一能用薛定谔相位因子得到的伽利略不变四分量旋量方程。讨论了所得结果的物理意义及其与泡利-薛定谔方程的关系。
英文摘要：
A search for fundamental (Galilean invariant) dynamical equations for two and four-component spinor wave functions is conducted in Galilean space-time. A dynamical equation is considered as fundamental if it is invariant under the symmetry operators of the group of the Galilei metric and if its state functions transform like the irreducible representations of the group of the metric. It is shown that there are no Galilean invariant equations for two-component spinor wave functions. A method to derive the Lévy-Leblond equation for a four-component spinor wave function is presented. It is formally proved that the Lévy-Leblond and Schrödinger equations are the only Galilean invariant four-component spinor equations that can be obtained with the Schrödinger phase factor. Physical implications of the obtained results and their relationships to the Pauli-Schrödinger equation are discussed.
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。
