粒子和场的对称性与非对易几何
Particle and Field Symmetries and Noncommutative Geometry
摘要：
非对易几何的发展为物理学创造了新的可能性。本文确定了在粒子和场的相互作用和基本对称性中出现的一些交换和导出结构。共存结构的要求及其一致性，产生了一个数学框架，作为基本物理理论的基础。粒子和场的量子理论的其他发展包括规范场的对称性和粒子的费米-玻色对称性。这些涉及规范协变推导和作用泛函;以及对易代数和Bogoliubov变换。非交换的Theta形式引入了一个附加的和基本的结构。本文得到了各种结构的相互关系，以及费米子/玻色子粒子与杨-米尔斯规范场相互作用的对称性条件。许多物理系统的例子正在被解决，数学形式主义正在被创建，以理解物理学的基本基础。
英文摘要：
The development of Noncommutative Geometry is creating a reworking and new possibilities in physics. This paper identifies some of the commutation and derivation structures that arise in particle and field interactions and fundamental symmetries. The requirements of coexisting structures, and their consistency, produce a mathematical framework that underlies a fundamental physics theory. Among other developments in Quantum theory of particles and fields are the symmetries of gauge fields and the Fermi-Bose symmetry of particles. These involve a gauge covariant derivation and the action functionals; and commutation algebras and Bogoliubov transforms. The non commutative Theta form introduces an additional and fundamental structure. This paper obtains the interrelations of various structures, and the conditions for the symmetries of Fermionic/Bosonic particles interacting with Yang Mills gauge fields. Many example physical systems are being solved, and the mathematical formalism is being created to understand the fundamental basis of physics.
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