论文标题
具有扭曲的真实结构的光谱三元三元的仪表转换
Gauge transformations of spectral triples with twisted real structures
论文作者
论文摘要
扭曲的真实结构有充分的动力，是实现狄拉克运算符的共形转换的一种方法，用于实际光谱三重，而无需扭转非交通型1形式。我们研究了光谱三元组与扭曲的真实结构的耦合，以衡量磁场，从而通过模块和双模型作为指导原理采用莫里塔等效性，并特别注意修改Dirac Operator的内部波动。特别是，我们分析了扭曲的一阶条件，作为放弃一阶条件以超越标准模型的可能替代方法，并相应地详细介绍了仪表变换的特殊情况。将形式主义应用于玩具模型时，我们认为在某些物理动机的假设下，基于左右对称代数的光谱三重应减少到基本粒子和相互作用的标准模型的频谱，如未扭转的情况。
Twisted real structures are well-motivated as a way to implement the conformal transformation of a Dirac operator for a real spectral triple without needing to twist the noncommutative 1-forms. We study the coupling of spectral triples with twisted real structures to gauge fields, adopting Morita equivalence via modules and bimodules as a guiding principle and paying special attention to modifications to the inner fluctuations of the Dirac operator. In particular, we analyse the twisted first-order condition as a possible alternative to abandoning the first-order condition in order to go beyond the Standard Model, and elaborate upon the special case of gauge transformations accordingly. Applying the formalism to a toy model, we argue that under certain physically-motivated assumptions the spectral triple based on the left-right symmetric algebra should reduce to that of the Standard Model of fundamental particles and interactions, as in the untwisted case.
