关于Dirac代数基无关计算的注记
Notes on basis-independent computations with the Dirac algebra
摘要：
在这些说明中，我们首先审查泡利的证明，他的“基本定理”，国家的等价性，任何两套狄拉克矩阵$\{ γ^μ\}$。由于这个定理，不仅狄拉克方程中的所有物理结果必须与狄拉克矩阵所选的基无关，而且在计算过程中不需要求助于特定的基也可以得到结果。事实上，我们证明了这一点的情况下，狄拉克旋量的行为下洛伦兹变换，量子化的狄拉克场，期望值的自旋算子和其他几个主题。特别强调了共轭狄拉克旋量定义中使用的矩阵$β$和$γ^0$的完全不同的物理和数学背景。最后，我们比较的基础上独立的操作与狄拉克矩阵的Weyl基础上进行。本笔记提供了一个自包含的介绍狄拉克理论，仅利用简单的狄拉克代数和权力的泡利定理。
英文摘要：
In these notes we first review Pauli's proof of his `fundamental theorem' that states the equivalence of any two sets of Dirac matrices $\{ γ^μ\}$. Due to this theorem not only all physical results in the context of the Dirac equation have to be independent of the basis chosen for the Dirac matrices, but it should also be possible to obtain the results without resorting to a specific basis in the course of the computation. Indeed, we demonstrate this in the case of the behaviour of Dirac spinors under Lorentz transformations, the quantization of the Dirac field, the expectation value of the spin operator and several other topics. In particular, we emphasize the totally different physics and mathematics background of the matrix $β$, used in the definition of the conjugate Dirac spinor, and $γ^0$. Finally, we compare the basis-independent manipulations with those performed in the Weyl basis of Dirac matrices. The present notes provide a self-contained introduction to the Dirac theory by solely exploiting the simplicity of the Dirac algebra and the power of Pauli's Theorem.
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