发表机构
Bogoliubov Laboratory of Theoretical Physics, JINR; Dubna State University（杜布纳联合核研究所理论物理实验室; 杜布纳国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了基于密度四脚场变量的多项式引力表述，发现其能极大简化标量-引力耦合，但无法产生有限物质-引力项的 realistic 模型。
AI 中文摘要
我们构建了一个基于四脚场的经典引力表述，该表述使得希尔伯特作用量在引力微扰下成为多项式形式，并识别出一些允许与这类微扰进行多项式耦合的物质模型。我们引入了密度四脚场变量，这些变量在保持显式局域洛伦兹标架的同时，将逆度规密度因子化。通过引入一个新的辅助场，可以构造一个关于这些变量及其微扰的多项式作用量。我们为该模型构建了BRST复形，并推导了传播子和相互作用规则。在四维中，具有标准动能项和势能的标量场允许与密度四脚场微扰存在有限数量的耦合项。在所有Horndeski引力模型中，只有很窄的一个子类允许与密度四脚场微扰进行多项式耦合。例如，爱因斯坦-标量-高斯-博内模型总是具有与密度四脚场微扰的无限塔相互作用。类似地，狄拉克费米子的标准动能项和矢量场的标准动能项都允许无限塔的相互作用。因此，密度四脚场变量为标量-引力耦合提供了极大的简化，但这种简化不足以产生一个具有有限数量物质-引力项的 realistic 模型。
英文摘要
We construct a classical formulation of gravity in terms of the vierbein that makes the Hilbert action polynomial in gravitational perturbations and identify some matter models that admit a polynomial coupling to such perturbations as well. We introduce the density vierbein variables that factorize the inverse metric density while retaining an explicit local Lorentz frame. With the introduction of a new auxiliary field, one can construct an action that is polynomial in such variables and their perturbations. Constructed the BRST complex for the model and derived propagators and interaction rules. In four dimensions, a scalar field with the canonical kinetic term and a potential admits a finite number of coupling terms with the density vierbein perturbations. Among all Horndeski gravity models, only a narrow subclass admits a polynomial coupling to the density vierbein perturbations. For instance, the Einstein--scalar--Gauss--Bonnet model always has an infinite tower of interactions with the density vierbein perturbation. Similarly, the standard kinetic term for the Dirac fermions and the standard kinetic term for a vector field both admit an infinite tower of interactions. Consequently, the density vierbein variables provide a great simplification for scalar-gravitational couplings, but the simplification is not strong enough to produce a realistic model with a finite number of matter-gravity terms.
