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Derivation-based noncommutative field theories on AF algebras
International Journal of Geometric Methods in Modern Physics ( IF 2.1 ) Pub Date : 2021-10-06 , DOI: 10.1142/s0219887821502133
T. Masson 1 , G. Nieuviarts 1
Affiliation  

In this paper, we start the investigation of a new natural approach to “unifying” noncommutative gauge field theories (NCGFT) based on approximately finite-dimensional (AF) C-algebras. The defining inductive sequence of an AF C-algebra is lifted to enable the construction of a sequence of NCGFT of Yang–Mills–Higgs types. This paper focuses on derivation-based noncommutative field theories. A mathematical study of the ingredients involved in the construction of a NCGFT is given in the framework of AF C-algebras: derivation-based differential calculus, modules, connections, metrics and Hodge *-operators, and Lagrangians. Some physical applications concerning mass spectra generated by Spontaneous Symmetry Breaking Mechanisms (SSBM) are proposed using numerical computations for specific situations.

中文翻译:

AF代数上基于导数的非交换场论

在本文中,我们开始研究一种基于近似有限维(一种F)C*-代数。定义的归纳序列一种F C*-代数被提升以能够构建杨-米尔斯-希格斯类型的 NCGFT 序列。本文重点研究基于导数的非交换场论。在以下框架中对构建 NCGFT 所涉及的要素进行了数学研究一种F C*-代数:基于推导的微积分、模块、连接、度量和 Hodge *-operators 和 Lagrangians。一些关于由自发对称破坏机制 (SSBM) 生成的质谱的物理应用是针对特定情况使用数值计算提出的。
更新日期:2021-10-06
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