具有双曲数的相对论量子物理
Relativistic quantum physics with hyperbolic numbers
摘要：
给出了二次Dirac方程和麦克斯韦方程组的三维泛复Clifford代数表示。研究了全代数的一个子集，它同构于Baylis代数.该方法基于庞加莱群的两个Casimir算子，质量算子和自旋算子，这与Pauli-Lubanski矢量有关。简要讨论了球面对称的推广。与贝利斯代数的结构差异表现在双曲单位的形状上，它在这种形式主义中起着不可或缺的作用。
英文摘要：
A representation of the quadratic Dirac equation and the Maxwell equations in terms of the three-dimensional universal complex Clifford algebra is given. The investigation considers a subset of the full algebra, which is isomorphic to the Baylis algebra. The approach is based on the two Casimir operators of the Poincare group, the mass operator and the spin operator, which is related to the Pauli-Lubanski vector. The extension to spherical symmetries is discussed briefly. The structural difference to the Baylis algebra appears in the shape of the hyperbolic unit, which plays an integral part in this formalism.
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