一些基本物理的几何推导
A brief geometric derivation of some fundamental physics
摘要：
从两个交换正交单位向量的简单起点出发，导出了物理学中的几个基本结果。这些单位矢量的组合导致球谐函数和Schwinger的第二量子化的角动量态的玻色子运营商的表达式。通过对单位向量的限制，可以将交换单位向量转化为反交换单位向量。这导致泡利自旋矩阵。通过引入双曲旋转，矢量可以被赋予有限范数，并得到了狭义相对论和狄拉克方程的结果，四动量的变化是由于四势的变化的假设导致了电磁场张量和洛伦兹力。将四元势视为受四元电流驱动的谐振子，得到了Mawell方程。从四动量的非相对论极限出发，得到了薛定谔方程。
英文摘要：
Several fundamental results in physics are derived from the simple starting point of two commuting orthogonal unit vectors. The combination of these unit vectors leads to spherical harmonics and Schwinger's expression of the second-quantized angular momentum states in terms of bosonic operators. Commuting unit vectors can be turned into anticommuting ones by the restriction to a single unit vector. This leads to Pauli spin matrices. By including hyperbolic rotations, vectors can be given a finite norm and results from special relativity and Dirac's equation are found. The assumption that the change in four-momentum is due to the change in four-potential leads to the electromagnetic field tensor and the Lorentz force. Mawell's equations are obtained by viewing the four-potential as an harmonic oscillator driven by the four-current. The Schrödinger equation is obtained from the nonrelativistic limit of the four-momentum.
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