arXiv 2602.200472026-02hep-thgr-qc

二次引力中的散射幅在一般形式化中

Scattering amplitudes in Quadratic Graivty in a general formalism

Instituto de Matemática Luis Santaló (IMAS)（路易斯·桑塔洛数学研究所）；CONICET（阿根廷国家科学研究委员会）

Osvaldo P. Santillán

备注：: Final version, accepted for publication in Nucl. Phys. B

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AI总结：

本文在一般形式化中推导了LSZ规则，针对高阶理论，确定引力子的产生湮灭模式，讨论了两种量化方法。

摘要：

在\cite{salvio}中，受\cite{pauli}-\cite{donogue}启发，提出了计算二次引力\cite{stelle1}-\cite{stelle2}相关函数的程序，并在\cite{salvio2}-\cite{salve}中进一步利用。通过构造，很可能该程序不与单位性冲突。相应的哈密顿量量子化基于非正定度量空间中的协变与反协变区分\cite{gross}。高阶理论的高斯-奥斯特罗格拉德斯基方法定义了两个动量密度$P_1$和$P_2$，以及两个坐标密度$Q_1$和$Q_2$，一对标准，另一对若产生湮灭代数标准则类似虚粒子，否则相反。\cite{salvio}中的方法涉及将虚粒子变量$P_2\to i P_2$和$Q_2\to i Q_2$延续到kets$|>$上取平均值后的作用。在本文中，遵循\cite{yomismo}，推导了LSZ规则，采用适应于完整四次或更高阶理论的形式化。主要技术点是确定适应当前程序的引力子产生湮灭模式。本文在此更一般背景下考虑。讨论了两种可能的量化，取决于该程序是否在LSZ计算开始或结束时应用。

英文摘要：

In \cite{salvio}, inspired by the works \cite{pauli}-\cite{donogue}, a prescription for calculating the correlation functions in Quadratic Gravity \cite{stelle1}-\cite{stelle2} was presented and further exploited in \cite{salvio2}-\cite{salve}. A covariant formalism ensuring positive definite probabilities is worked out, which is the main drawback of Quadratic Gravity. The Gauss-Ostrogradsky method for Quadratic Gravity defines two momentum densities $P_1$ and $P_2$ and two coordinate densities $Q_1$ and $Q_2$, one pair is standard, the other ghost like. The approach in \cite{salvio} involves the continuation $P_2\to i P_2$ and $Q_2\to i Q_2$ of the ghost variables acting on kets $|>$ after taking mean values. The notable result is that, in the euclidean setting, this procedure leads to Quadratic Gravity path integral $Z(J)$, thus renormalizability is not spoiled. In view of these findings, it is natural to ask how the LSZ rules of the model have to be formulated, and this is the topic of the present work. A formalism adapted to full quartic or higher order theories is worked out, extending the results of \cite{yomismo}. The main technical point is to determine the creation annihilation algebra for the graviton modes, adapted to the present prescription, and properly dealing with gauge symmetry. This makes the problem harder than the quantization of the Pais-Uhlenbeck model. Two possible quantization schemes are discussed, they depend on whether the above prescriptions are applied at the beginning or at the end of the LSZ calculation.

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