论文标题
标量量子场在Minkowski时空上的定位
Localization of scalar quantum fields on Minkowski space-time
论文作者
论文摘要
以一般时空和时间操作员的形式引入了针对克莱恩 - 戈登粒子状态的新定位方案。这些运算符的定义是通过在我们要本地化的标准场的动量空间中建立第二个量子场（在这里Klein-Gordon字段）来实现的。在动量空间中定义新领域的动机如下。在标准场理论中，人们可以为场激发定义动量（和能量）算子，而不能为一般位置（和时间）操作员定义一个算子，因为该场在位置空间中满足微分方程，并通过其傅立叶变换，在动量空间中一个代数方程。因此，在相反的田间理论中，即它在动量空间中满足微分方程和位置空间中的代数方程，我们将能够定义位置和时间操作员。由于新领域居住在克莱恩 - 戈登场的动量空间中，前者的创建/歼灭操作员会建立新的空间和时间操作员，并减少了后者的现场运营商。结果，克莱恩 - 戈登场的粒子状态是新空间和时间操作员的本征状态，因此位于其光谱所描述的时空上。最后，我们表明这个时空是平坦的，因为它适合了两个特殊相对论的假设。还提供了特殊相对论概念为惯性观察者和新领域的适当加速度的解释。
A new localization scheme for Klein-Gordon particle states is introduced in the form of general space and time operators. The definition of these operators is achieved by establishing a second quantum field in the momentum space of the standard field we want to localize (here Klein-Gordon field). The motivation for defining a new field in momentum space is as follows. In standard field theories one can define a momentum (and energy) operator for a field excitation but not a general position (and time) operator because the field satisfies a differential equation in position space and, through its Fourier transform, an algebraic equation in momentum space. Thus, in a field theory which does the opposite, namely it satisfies a differential equation in momentum space and an algebraic equation in position space, we will be able to define a position and time operator. Since the new field lives in the momentum space of the Klein-Gordon field, the creation/annihilation operators of the former, which build the new space and time operators, reduce to the field operators of the latter. As a result, particle states of Klein-Gordon field are eigenstates of the new space and time operators and therefore localized on a space-time described by their spectrum. Finally, we show that this space-time is flat because it accommodates the two postulates of special relativity. Interpretation of special relativistic notions as inertial observers and proper acceleration in terms of the new field is also provided.
