论文标题
动量量规场和非交通时空
Momentum Gauge Fields and Non-Commutative Space-Time
论文作者
论文摘要
在这项工作中，我们提出了一个规格原理，该原理从位置操作员的动量空间表示（$ {\ hat x} _i = i \ hbar \ hbar \ frac {\ partial} {\ partial} {\ partial p_i} $），而不是从动量操作员的位置空间表示（$ {\ hat p p} _i = -ii = -ii = -hbar \ frac {\ partial} {\ partial x_i} $）。我们讨论了这种新型量规理论的一些简单示例：（i）在此动量规程理论中，来自普通量规理论的模拟解决方案，（ii）使用动量量规场的Landau级别，（iii）来自动量量规场的非交换空间时间的出现。我们发现，非共同的时空参数可以取决于动量，并且可以构建一个模型，其中时空在低动量下是交换性的，但在高动量下会变得不相同。
In this work we present a gauge principle that starts with the momentum space representation of the position operator (${\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.
