论文标题
洛伦兹 - 融合的采样理论
Lorentz-covariant sampling theory for fields
论文作者
论文摘要
抽样理论是通过离散样品集的连续信号重建的通信工程学科。从物理学的角度来看，这对于时空是在普朗克量表上是连续还是离散的问题，这很有趣，因为在抽样理论中，我们具有可以将其视为等效地依赖连续或离散空间的功能。此外，可以制定采样的类似物，这些类似物会产生离散性的情况，而不会干扰潜在的时空对称性。特别是，有一个建议如何适应Minkowski时空的建议。在这里，我们将对采样理论的扩展到这种情况进行详细研究。我们还将一般讨论时空对称性如何在抽样理论中表现出来，从表面上看，这似乎与采样的离散性并不显着协变。具体而言，我们将展示如何具有采样属性的功能空间的对称性等效于存在与对称转换相关的可能采样晶格家族。
Sampling theory is a discipline in communications engineering involved with the exact reconstruction of continuous signals from discrete sets of sample points. From a physics perspective, this is interesting in relation to the question of whether spacetime is continuous or discrete at the Planck scale, since in sampling theory we have functions which can be viewed as equivalently residing on a continuous or discrete space. Further, it is possible to formulate analogues of sampling which yield discreteness without disturbing underlying spacetime symmetries. In particular, there is a proposal for how this can be adapted for Minkowski spacetime. Here we will provide a detailed examination of the extension of sampling theory to this context. We will also discuss generally how spacetime symmetries manifest themselves in sampling theory, which at the surface seems in conflict with the fact that the discreteness of the sampling is not manifestly covariant. Specifically, we will show how the symmetry of a function space with a sampling property is equivalent to the existence of a family of possible sampling lattices related by the symmetry transformations.
