Superoscillating functions are band-limited functions that can oscillate faster than their fastest Fourier component. The study of the evolution of superoscillations as initial datum of field equations requires the notion of supershift, which generalizes the concept of superoscillations. The present paper has a dual purpose. The first one is to give an updated and self-contained explanation of the strategy to study the evolution of superoscillations by referring to the quantum-mechanical Schrodinger equation and its variations. The second purpose is to treat the Dirac equation in relativistic quantum theory. The treatment of the evolution of superoscillations for the Dirac equation can be deduced by recent results on the Klein–Gordon equation, but further additional considerations are in order, which are fully described in this paper.

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狄拉克场中超振荡的演化

超振荡函数是带限函数，可以比最快的傅立叶分量振荡得更快。作为场方程初始数据的超振荡演化的研究需要超移的概念，它概括了超振荡的概念。本文有双重目的。第一个是通过参考量子力学薛定谔方程及其变体，对研究超振荡演化的策略进行更新和独立的解释。第二个目的是处理相对论量子理论中的狄拉克方程。狄拉克方程的超振荡演化的处理可以通过 Klein-Gordon 方程的最新结果推断出来，但进一步的额外考虑是有序的，这在本文中进行了充分描述。