论文标题
来自特殊约旦背景和光谱三元的粒子模型
Particle models from special Jordan backgrounds and spectral triples
论文作者
论文摘要
我们提出了基于约旦坐标代数的光谱三元组和代数背景的定义。我们还提出了波动的狄拉克运算符的天然和量规不变的骨配置空间，并将其计算为一般，几乎缔合的约旦，坐标代数。我们强调，即使坐标代数是$ c^*$ - 代数的自我伴侣部分，即使坐标为代数的一部分，也不等于通常的关联非共同几何形状。特别是，在约旦案例中，仪表场始终是单模型的，因此可以解决非交通性几何形状中的长期问题。
We put forward a definition for spectral triples and algebraic backgrounds based on Jordan coordinate algebras. We also propose natural and gauge-invariant bosonic configuration spaces of fluctuated Dirac operators and compute them for general, almost-associative, Jordan, coordinate algebras. We emphasize that the theory so obtained is not equivalent with usual associative noncommutative geometry, even when the coordinate algebra is the self-adjoint part of a $C^*$-algebra. In particular, in the Jordan case, the gauge fields are always unimodular, thus curing a long-standing problem in noncommutative geometry.
