普适耦合大质量引力，III：dRGT-Maheshwari纯自旋- $2$，Ogievetsky-Polubarinov和任意质量项
Universally Coupled Massive Gravity, III: dRGT-Maheshwari Pure Spin-$2$, Ogievetsky-Polubarinov and Arbitrary Mass Terms
摘要：
爱因斯坦方程是在20世纪50 - 70年代由多位作者利用万有耦合推导出的自由无质量自旋$2$场的方程;包括引力在内的总应力-能量是线性自由场方程的来源。在1960年代后期，Freund、Maheshwari和Schonberg也衍生出了一个巨大的变体，并被认为是独一无二的。万向联轴器有多宽？在过去的十年中，四个大质量自旋- $2$理论的$1$参数族（几乎任何密度权重的逆变、协变、四元组和协四元组）已经使用万有耦合导出。（共）四元衍生物包括德拉姆、加巴达泽和托利的三个纯自旋$2$理论中的两个;这两个理论首先出现在$2$ -参数Ogievetsky-Polubarinov家族（1965）中，该家族发展了度规的对称平方根作为非线性群实现。两个理论中的一个在1971 ~ 1972年被马赫什瓦里确认为纯自旋$2$，从而在它被宣布时避开了博尔韦尔-德塞尔-秋廷-弗拉德金幽灵。与前4类不同，本文允许非线性域的重定义来建立有效的度量。通过不坚持预先知道引力子势对所有阶的可观测意义，人们发现可以使用万有耦合导出任意引力子质量项。普遍耦合的质量/自相互作用项的任意性与爱因斯坦动力学项的唯一性形成鲜明对比。人们可能希望用万有耦合作为打破平局的标准，在更重要的理由（如没有鬼和有一个光滑的无质量极限）上选择同样令人满意的理论。但是普适耦合的普遍性意味着这个标准并不支持那些具有爱因斯坦动力学项的理论。
英文摘要：
Einstein's equations were derived for a free massless spin-$2$ field using universal coupling in the 1950-70s by various authors; total stress-energy including gravity's served as a source for linear free field equations. A massive variant was likewise derived in the late 1960s by Freund, Maheshwari and Schonberg, and thought to be unique. How broad is universal coupling? In the last decade four $1$-parameter families of massive spin-$2$ theories (contravariant, covariant, tetrad, and cotetrad of almost any density weights) have been derived using universal coupling. The (co)tetrad derivations included 2 of the 3 pure spin-$2$ theories due to de Rham, Gabadadze, and Tolley; those two theories first appeared in the $2$-parameter Ogievetsky-Polubarinov family (1965), which developed the symmetric square root of the metric as a nonlinear group realization. One of the two theories was identified as pure spin-$2$ by Maheshwari in 1971-2, thus evading the Boulware-Deser-Tyutin-Fradkin ghost by the time it was announced. Unlike the previous 4 families, this paper permits _nonlinear_ field redefinitions to build the effective metric. By not insisting in advance on knowing the observable significance of the graviton potential to all orders, one finds that an _arbitrary_ graviton mass term can be derived using universal coupling. The arbitrariness of a universally coupled mass/self-interaction term contrasts sharply with the uniqueness of the Einstein kinetic term. One might have hoped to use universal coupling as a tie-breaking criterion for choosing among theories that are equally satisfactory on more crucial grounds (such as lacking ghosts and having a smooth massless limit). But the ubiquity of universal coupling implies that the criterion doesn't favor any particular theories among those with the Einstein kinetic term.
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