标题： 动量规范场与非对易时空 显示英文标题

标题： Momentum Gauge Fields and Non-Commutative Space-Time

摘要： 在本工作中，我们提出了一种规范原理，该原理从位置算符的动量空间表示（${\hat x}_i = i \hbar \frac{\partial}{\partial p_i}$）出发，而不是从动量算符的位置空间表示（${\hat p}_i = -i \hbar \frac{\partial}{\partial x_i}$）出发。 我们讨论了这种新型规范理论的一些简单例子：（i）从普通规范理论中得到的类比解，在此动量规范理论中；（ii）使用动量规范场的兰道能级；（iii）从动量规范场中出现非对易时空。 我们发现非对易时空参数可以依赖于动量，并且可以构建一个模型，在低动量下时空是对易的，但在高动量下变得非对易。 显示英文摘要

摘要： In this work we present a gauge principle that starts with the momentum space representation of the position operator (${\hat x}_i = i \hbar \frac{\partial}{\partial p_i}$) rather than starting with the position space representation of the momentum operator (${\hat p}_i = -i \hbar \frac{\partial}{\partial x_i}$). We discuss some simple examples with this new type of gauge theory: (i) analog solutions from ordinary gauge theory in this momentum gauge theory, (ii) Landau levels using momentum gauge fields, (iii) the emergence of non-commutative space-times from the momentum gauge fields. We find that the non-commutative space-time parameter can be momentum dependent, and one can construct a model where space-time is commutative at low momentum but becomes non-commutative at high momentum.