标题： 标量场的聚合量子化中Wightman函数时空离散性的出现 显示英文标题

标题： Emergence of spacetime discreteness in Wightman function from polymer quantization of scalar field

摘要： Wightman函数，即真空两点函数，在福克量子化中对于无质量自由标量场与对应时空点之间的不变距离平方成反比。 当这两个点被取为无限接近时，它自然会发散。 通过结合分析和数值方法，我们证明在标量场的聚合物量子化中，Wightman函数有上界。 Wightman函数的有界值由聚合物尺度决定，其有界性可以看作是时空具有零点长度。 这种时空有效离散性的出现仅来自于物质场的聚合物量子化，因为几何被当作经典处理。 这也表明，物质场的聚合物量子化本身可以捕捉有效离散几何的某些方面。 我们讨论了该结果对依赖于Wightman函数性质的Unruh-DeWitt探测器响应函数的影响。 显示英文摘要

摘要： The Wightman function i.e. vacuum two-point function, for a massless free scalar field in Fock quantization is inversely proportional to the invariant distance squared between the corresponding spacetime points. Naturally it diverges when these two points are taken to be infinitesimally close to each other. Using a combination of analytical and numerical methods, we show that the Wightman function is bounded from above in polymer quantization of scalar field. The bounded value of the Wightman function is governed by the polymer scale and its bounded nature can be viewed as if the spacetime has a zero-point length. This emergence of effective discreteness in spacetime appears from polymer quantization of matter field alone as the geometry is treated classically. It also demonstrates that the polymer quantization of matter field itself can capture certain aspects of the effective discrete geometry. We discuss the implications of the result on the response function of a Unruh-DeWitt detector that depends on the properties of the Wightman function.