论文标题
从弯曲的动量空间到kaluza-klein降低的动量量规场
Momentum gauge fields from curved momentum space through Kaluza-Klein reduction
论文作者
论文摘要
在这项工作中，我们研究了弯曲动量空间与动量依赖量规场之间的关系。尽管前者是一个经典的思想，已被证明与最小长度模型相关，但后者构成了量子重力现象学的相对较新的发展。特别是，量规原理在动量空间中的定位均需修改$ \ hat {x}^μ\ rightArrow \ hat {x}^}^μ-g a^μ（\ hat {p}）$ aky to poguge-covariant在瞬间的衍生产品中，以根据微小的划分，在这里，我们通过在动量空间中表现出曲率的高维几何形状的kaluza-klein降低来得出这两种作用。新兴量规场的相互作用以及其余的弯曲动量空间导致了海森贝格代数的修改。仪表场表示摩氨型非构型取决于模拟场强度张量，而尺寸降低的弯曲动量空间几何形状转化为Snyder型的非交通性几何形状。
In this work we investigate the relation between curved momentum space and momentum-dependent gauge fields. While the former is a classic idea that has been shown to be tied to minimal-length models, the latter constitutes a relatively recent development in quantum gravity phenomenology. In particular, the gauge principle in momentum space amounts to a modification of the position operator of the form $\hat{X}^μ\rightarrow\hat{X}^μ-g A^μ(\hat{P})$ akin to a gauge-covariant derivative in momentum space according to the minimal coupling prescription. Here, we derive both effects from a Kaluza-Klein reduction of a higher-dimensional geometry exhibiting curvature in momentum space. The interplay of the emerging gauge fields as well as the remaining curved momentum space lead to modifications of the Heisenberg algebra. While the gauge fields imply Moyal-type noncommutativity dependent on the analogue field strength tensor, the dimensionally reduced curved momentum space geometry translates to a Snyder-type noncommutative geometry.
