AI 中文总结
研究振荡子散射模式至Fodor展开前三个阶次，用初等函数表示，用于完全分解场并解析求逆，在量子场论中证明产生和湮灭算子满足振子代数，扩展相关证明到相对论模式。
AI 中文摘要
我们给出了振荡子散射模式，精确到Fodor展开的前三个阶次，用初等函数表示。对于相对论模式，这些结果是新的。我们用它们来完全分解场，并对分解进行解析求逆。在量子场论中，这使我们能够证明相应的产生和湮灭算子满足通常的振子代数，将在Fodor展开固定阶次下存在周期振荡子态的证明扩展到相对论模式。
英文摘要
We present the scattering modes of the oscillon, to the first three orders in the Fodor expansion, in terms of elementary functions. In the case of relativistic modes, these results are new. We use them to fully decompose the field and also to analytically invert the decomposition. In quantum field theory, this allows us to show that the corresponding creation and annihilation operators satisfy the usual oscillator algebra, extending to relativistic modes the demonstration that, at a fixed order in the Fodor expansion, a periodic oscillon state exists.
Comments23 pages, 2 figures
