适用于状态依赖无穷导数引力的协变曲率-历史场形式化
A Covariant Curvature-History Field Formulation for State-Dependent Infinite-Derivative Gravity
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中文总结 AI 辅助
本研究针对状态依赖无穷导数引力构建协变辅助场形式化，用局域标量场C(x)替代依赖曲线的历史变量，推导耦合场方程并证明应力-能量交换在壳抵消，确保应力-能量张量协变守恒。
中文摘要 AI 辅助
我们为状态依赖无穷导数引力构建了一种协变辅助场形式化。零测地线曲率-历史积分为状态依赖提供了自然的动机，但在存在焦散和分支变化时，它们会出现变分歧义并失去对光滑度规的依赖。我们将依赖曲线的历史变量替换为满足由Kretschmann不变量源项的协变双曲方程的局域标量场C(x)。通过共轭辅助场χ(x)在作用量层面强制执行历史方程。由于动力学非局域尺度依赖于C(x)，非局域形因子的变分涉及非对易算子，该变分使用Duhamel公式计算。将C和χ视为独立局域场，我们推导了耦合场方程，并表明非局域记忆部分与辅助历史部分之间的应力-能量交换在壳上抵消。所得的局域诺特定理恒等式确保了组合记忆-历史应力-能量张量的协变守恒，并满足收缩比安基恒等式。
英文摘要
We construct a covariant auxiliary-field formulation for state-dependent infinite-derivative gravity. Null-congruence curvature-history integrals provide a natural motivation for state dependence, but they suffer from variational ambiguities and loss of smooth metric dependence in the presence of caustics and branch changes. We replace the curve-dependent history variable by a local scalar field \(C(x)\) satisfying a covariant hyperbolic equation sourced by the Kretschmann invariant. The history equation is enforced at the level of the action by a conjugate auxiliary field \(χ(x)\). Since the dynamical nonlocality scale depends on \(C(x)\), the variation of the nonlocal form factor involves noncommuting operators; this variation is evaluated using Duhamel's formula. Treating \(C\) and \(χ\) as independent local fields, we derive the coupled field equations and show that the stress-energy exchange between the nonlocal memory sector and the auxiliary history sector cancels on shell. The resulting local Noether identity ensures covariant conservation of the combined memory-history stress-energy tensor and compatibility with the contracted Bianchi identity.
