空间反转、时间反转和电荷共轭的群论描述
Group Theoretical Description of Space Inversion, Time Reversal and Charge Conjugation
摘要：
给出了基本离散对称性（空间反演P、时间反演T和电荷共轭C）的群论描述。利用Clifford代数的基本自同构，研究了实数域和复数域上多维空间正交群的离散子群。根据除环的结构，对实数域和复数域上的Clifford代数建立了自同构群的完全分类。利用Clifford代数的旋量表示研究了真正交Lorentz群的二维表示。实数，复数，四元数和八元数表示的洛伦兹群被认为是。Atiayh-Bott-Shapiro周期定义在Lorentz群上。介绍了洛伦兹群的商表示。结果表明，商表示是最适合的描述无质量的物理场。给出了基本物理场的代数构造。
英文摘要：
A group theoretical description of basic discrete symmetries (space inversion P, time reversal T and charge conjugation C) is given. Discrete subgroups of orthogonal groups of multidimensional spaces over the fields of real and complex numbers are considered in terms of fundamental automorphisms of Clifford algebras. In accordance with a division ring structure, a complete classification of automorphism groups is established for the Clifford algebras over the fields of real and complex numbers. Finite-dimensional representations of the proper orthochronous Lorentz group are studied in terms of spinor representations of the Clifford algebras. Real, complex, quaternionic and octonionic representations of the Lorentz group are considered. The Atiayh-Bott-Shapiro periodicity is defined on the Lorentz group. Quotient representations of the Lorentz group are introduced. It is shown that quotient representations are the most suitable for description of massless physical fields. An algebraic construction of basic physical fields is presented.
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