相对论性泡利方程
The relativistic Pauli equation
摘要：
在讨论了C2和复2 × 2矩阵的代数可以用于表示非相对论旋转和洛伦兹变换的方式之后，我们证明了Dirac双旋量可以更有利地表示为2 × 2复矩阵。这样就可以给狄拉克方程一种矩阵值波函数的形式，这种形式不再需要引入伽马矩阵或选择它们的表示。外电磁场中带电自旋粒子的最小耦合Dirac方程则意味着矩阵值波函数中的Klein-Gordon型二阶方程，代表Pauli方程的相对论模拟。最后，我们提出了相对论性泡利方程的拉格朗日形式。
英文摘要：
After discussing the way that C2 and the algebra of complex 2x2 matrices can be used for the representation of both non-relativistic rotations and Lorentz transformations, we show that Dirac bispinors can be more advantageously represented as 2x2 complex matrices. One can then give the Dirac equation a form for such matrix-valued wave functions that no longer necessitates the introduction of gamma matrices or a choice for their representation. The minimally-coupled Dirac equation for a charged spinning particle in an external electromagnetic field then implies a second order equation in the matrix-valued wave functions that is of Klein-Gordon type and represents the relativistic analogue of the Pauli equation. We conclude by presenting the Lagrangian form for the relativistic Pauli equation.
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