论文标题
$κ$ -Minkowski空间上的量表理论：扭曲和模块化操作员
Gauge theories on $κ$-Minkowski spaces: Twist and modular operators
论文作者
论文摘要
我们讨论了$κ$-POINCARé不变式动作的构建，用于$κ$ -Minkowski空间。我们考虑各种类别的不弯曲和（BI）扭曲的差分计算。 Starting from a natural class of noncommutative differential calculi based on a particular type of twisted derivations belonging to the algebra of deformed translations, combined with a twisted extension of the notion of connection, we prove an algebraic relation between the various twists and the classical dimension d of the $κ$-Minkowski space(-time) ensuring the gauge invariance of the candidate actions for gauge theories.我们表明，在自然的微积分中，基于杰出的扭曲派生集，d = 5是量规动作支持量规不变性和$κ$-POINCARé不变性的经典维度的独特值。在标准（未扭曲的）差分计算中，我们表明无法实现完整的规格不变性，尽管在一组受到模块化（tomita）操作员限制的转换下的不变性，这些操作员仍源于$κ$-POINCARé不变性。
We discuss the construction of $κ$-Poincaré invariant actions for gauge theories on $κ$-Minkowski spaces. We consider various classes of untwisted and (bi)twisted differential calculi. Starting from a natural class of noncommutative differential calculi based on a particular type of twisted derivations belonging to the algebra of deformed translations, combined with a twisted extension of the notion of connection, we prove an algebraic relation between the various twists and the classical dimension d of the $κ$-Minkowski space(-time) ensuring the gauge invariance of the candidate actions for gauge theories. We show that within a natural differential calculus based on a distinguished set of twisted derivations, d=5 is the unique value for the classical dimension at which the gauge action supports both the gauge invariance and the $κ$-Poincaré invariance. Within standard (untwisted) differential calculi, we show that the full gauge invariance cannot be achieved, although an invariance under a group of transformations constrained by the modular (Tomita) operator stemming from the $κ$-Poincaré invariance still holds.
