Abstract

We review and elaborate on some aspects of the classically scale-invariant renormalizable \(4\)-derivative scalar theory \(L=\phi\,\partial^4\phi+g(\partial\phi)^4\). Similar models appear, e.g., in the context of conformal supergravity or in the description of the crystalline phase of membranes. Considering this theory in Minkowski signature, we suggest how to define Poincaré-invariant scattering amplitudes by assuming that only massless oscillating (nongrowing) modes appear as external states. In such shift-symmetric interacting theory, there are no IR divergences despite the presence of \(1/q^4\) internal propagators. We discuss how nonunitarity of this theory manifests itself at the level of the one-loop massless scattering amplitude.

中文翻译：

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对 4 维 4 导数标量理论的评论

摘要

我们回顾并详细阐述了经典尺度不变可重正化\(4\)导数标量理论\(L=\phi\,\partial^4\phi+g(\partial\phi)^4\) 的某些方面。类似的模型出现在例如共形超重力的背景下或在膜的结晶相的描述中。考虑到闵可夫斯基签名中的这一理论，我们建议如何通过假设只有无质量振荡（非增长）模式作为外部状态出现来定义庞加莱不变散射振幅。在这种位移对称相互作用理论中，尽管存在\(1/q^4\)内部传播子，但不存在IR发散。我们讨论该理论的非齐性如何在单环无质量散射振幅的水平上表现出来。