Majid-Ruegg模型和普朗克尺度
The Majid-Ruegg model and the Planck scales
摘要：
在kappa-Minkowski空间中引入了一种新的具有中心内积的微分学.“坏”行为的微分讨论辛量子化和A-无限代数。在薛定谔方程中使用这种微积分可以得到两个值，可以与普朗克质量和长度进行比较。这种比较给出了kappa-Minkowski空间中变形参数的近似数值。我们提出的数值证据表明，有一个潜在的可观察到的克莱因-戈登方程的传播速度的变化。修正的电动力学方程（无旋量场）是从非对易协变导数导出的。我们注意到，这些方程表明光速与频率无关，这与KG的结果相反（需要注意的是，零电流与真空中的电流不同）。最后，我们对与量子理论和引力（不一定是量子引力）以及非对易几何有关的测量进行了一些哲学评论。
英文摘要：
A novel differential calculus with central inner product is introduced for kappa-Minkowski space. The `bad' behaviour of this differential calculus is discussed with reference to symplectic quantisation and A-infinity algebras. Using this calculus in the Schrodinger equation gives two values which can be compared with the Planck mass and length. This comparison gives an approximate numerical value for the deformation parameter in kappa-Minkowski space. We present numerical evidence that there is a potentially observable variation of propagation speed in the Klein-Gordon equation. The modified equations of electrodynamics (without a spinor field) are derived from noncommutative covariant derivatives. We note that these equations suggest that the speed of light is independent of frequency, in contrast to the KG results (with the caveat that zero current is not the same as in vacuum). We end with some philosophical comments on measurement related to quantum theory and gravity (not necessarily quantum gravity) and noncommutative geometry.
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