双标量-张量理论：一种空间协变引力方法
Bi-scalar-tensor theory: a spatially covariant gravity approach
- School of Physics, Sun Yat-sen University（中山大学物理学院）
- Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing, Sun Yat-sen University（中山大学广东省量子计量与传感重点实验室）
- Department of Physics, Rikkyo University（立教大学物理系）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文提出一种从空间协变引力出发构造无鬼魅高阶导数标量-张量理论的新方法，通过哈密顿约束分析给出消除额外标量模式的简并条件，从而系统构建双/多标量-张量理论。
中文摘要 AI 辅助
我们提出了一种构造无鬼魅多场高阶导数标量-张量理论的新方法。其思想是从空间协变引力出发，并将其与一个额外的标量场耦合。得到的空间协变标量场理论可以被理解为在一个标量的幺正规范下的双标量-张量理论。在度规速度通过外曲率进入、额外标量通过直至二阶的时间导数进入的广泛类别中，我们进行了哈密顿约束分析。我们证明该理论通常传播五个物理自由度（DOFs），即两个张量模式和三个标量模式。其中一个标量模式是与额外标量相关的不期望的模式。然后我们推导出一个简并条件和一个附加的一致性条件。当两个条件都成立时，不期望的模式被消除，理论传播四个自由度。由此产生的理论分为两种情况，取决于三级约束的保持是否在没有新约束的情况下闭合，还是产生一个四级约束。我们还研究了双场不形变换，推导了其可逆性条件，并在幺正规范下表达。我们的构造为构建具有高阶导数的双标量-张量和多标量-张量理论提供了一种系统方法。
英文摘要
We propose a novel method for constructing ghost-free multi-field higher-derivative scalar-tensor theories. The idea is to start from spatially covariant gravity and couple it to an additional scalar field. The resulting spatially covariant scalar field theory can be understood as a bi-scalar-tensor theory in the unitary gauge of one scalar. Within a broad class in which metric velocities enter through the extrinsic curvature and the additional scalar enters through temporal derivatives up to second order, we perform a Hamiltonian constraint analysis. We show that the theory generally propagates five physical degrees of freedom (DOFs), i.e., two tensor modes and three scalar modes. One of the scalar modes is the unwanted mode associated with the additional scalar. We then derive a degeneracy condition and an additional consistency condition. When both conditions hold, the unwanted mode is eliminated and the theory propagates four degrees of freedom. The resulting theories fall into two cases, depending on whether the preservation of the tertiary constraint closes without a new constraint or generates a quaternary constraint. We also study the two-field disformal transformation, derive its invertibility condition, and express it in the unitary gauge. Our construction provides a systematic approach to constructing bi- and multi-scalar-tensor theories with higher derivatives.
