论文标题
适当的时间操作员及其不确定性关系
Proper time operator and its uncertainty relation
论文作者
论文摘要
我们在适当的时间内研究振荡器的量子特性。适当的时间振荡器是具有质量的粒子模型。它的内部时间可以视为自我伴侣操作员。振荡器的流离时间和移位时间率遵守了一个不确定性关系，类似于位置和动量之间的关系，这与通常的能量时间不确定性关系不同。此外，我们证明了具有适当时间振荡器的物质字段满足klein-gordon方程。它具有零自旋量子场的属性。采用的配方允许物质领域的时间和空间之间进行更对称的处理。
We study the quantum properties of an oscillator in proper time. This proper time oscillator is a particle model with mass that is on shell. Its internal time can be treated as a self-adjoint operator. The displaced time and displaced time rate of the oscillator obey an uncertainty relation resembling the one between position and momentum, which is different from the usual energy-time uncertainty relation. In addition, we demonstrate that a matter field with proper time oscillators satisfies the Klein-Gordon equation. It has properties of a zero-spin quantum field. The formulations adopted permits a more symmetrical treatment between time and space in a matter field.
