狄拉克方程及其推广在粒子物理中的应用
Some examples of uses of Dirac equation and its generalizations in particle physics
摘要：
考虑了具有反常磁矩的狄拉克方程在描述电子、μ子和夸克特性中的应用。本文将四维标量势和矢量势的Dirac方程化为适合于数值积分的形式。当选择某种势时，解可以近似强子内部的夸克态。考虑到夸克在禁闭域中的复杂行为，我们考虑了Dirac-Gursey-Lee方程，五维Minkowski空间中的Dirac方程，量子相空间中的Dirac方程等推广。Dirac方程及其推广的扩展对称性被认为是，它可以用于调查这些方程的解的性质和随后在粒子物理中的应用。
英文摘要：
Applications of the Dirac equation with an anomalous magnetic moment are considered for description of characteristics of electrons, muons and quarks. The Dirac equation with four-dimensional scalar and vector potentials is reduced to a form suitable for a numerical integration. When a certain type of the potential is chosen, solutions can approximate quark states inside hadrons. In view of complicated behaviour of quarks in a confinement domain some generalizations are considered such as the Dirac-Gursey-Lee equation, the Dirac equation in a five-dimensional Minkowski space, the Dirac equation in a quantum phase space. Extended symmetries for the Dirac equation and its generalizations are considered, which can be used for investigation of properties of solutions of these equations and subsequent applications in particle physics.
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