论文标题
重力量化的量化
Quantization of measure in gravitation
论文作者
论文摘要
使用有关任何两种度量之间的关系以及在循环量子重力中使用的方法的ra子 - 尼克比定理，这表明在重力中，可以量化任何甚至与度量无关的措施。我们认为，两个度量运算符（radon-nikodym衍生物）之间的比例系数是某种函数。结果是，在度量的换向关系的右侧，基本长度变成了可变数量，这可能会导致平滑奇异性。也正在讨论ra子 - 尼克比衍生物是操作员的情况。正在考虑具有量子测量的空间背景的经典和量子理论。
Using the Radon-Nikodym theorem concerning the relation between any two measures, as well as the methods employed in loop quantum gravity, it is shown that, in gravitation, one can quantize any measure which is not even associated with metric. We have considered the simplest case where the proportionality coefficient between two operators of measure (the Radon-Nikodym derivative) is some function. The result is that in the right-hand side of the commutation relations for the measure the fundamental length becomes a variable quantity, and this can lead to smoothing the singularity. The case where the Radon-Nikodym derivative is an operator is also under discussion. Classical and quantum theories on the background of space endowed with quantum measure are under consideration.
