量子波动方程的广义Madelung变换I：场空间的广义球坐标
Generalized Madelung transformations for quantum wave equations I: generalized spherical coordinates for field spaces
摘要：
量子波函数取值的空间的马德隆变换从复数推广到包含群轨道的场空间，这些群轨道与球面同构。由此产生的实波方程的一般形式则涉及与群作用相关的矩阵代数的结构常数。复数代数、四元数代数和复四元数代数的特殊情况，分别与克莱因-戈登方程、相对论性泡利方程和双狄拉克方程有关，然后进行讨论。
英文摘要：
The Madelung transformation of the space in which a quantum wave function takes its values is generalized from complex numbers to include field spaces that contain orbits of groups that are diffeomorphic to spheres. The general form for the resulting real wave equations then involves structure constants for the matrix algebra that is associated with the group action. The particular cases of the algebras of complex numbers, quaternions, and complex quaternions, which pertain to the Klein-Gordon equation, the relativistic Pauli equation, and the bi-Dirac equation, resp., are then discussed.
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