迈向作用量依赖的帕拉蒂尼引力的联络形式化
Towards a Connection Formulation of Action-Dependent Palatini Gravity
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中文总结 AI 辅助
本研究将一阶帕拉蒂尼引力表述为作用量依赖的赫尔格洛茨场论，分析SO(1,3)规范联络的分解，发现存在可光滑参数化的摩擦场理论模空间，其壳上动力学均能重现一阶帕拉蒂尼引力。
中文摘要 AI 辅助
已有研究表明，一阶帕拉蒂尼引力可被表述为非保守的赫尔格洛茨（Herglotz）拉格朗日场论，该理论将共形模排除在其动力学变量空间之外。本研究分析了SO(1,3)规范联络在构建此作用量依赖理论中的作用。该联络可分解为“形状”部分与“标度”部分，其中仅前者保留在赫尔格洛茨理论中，而后者被纳入作用量依赖部分。研究表明，联络的分解选择是一个可被光滑参数化的空间，这一发现引出了“摩擦场理论的模空间”的存在，其中每个点对应于形状与标度联络动力学的不同拆分。在该模空间内的移动会在不同赫尔格洛茨拉格朗日之间转换，这些拉格朗日的壳上动力学均能重现一阶帕拉蒂尼引力，其区别在于原理论标度动力学的重现方式在作用量依赖与动力学挠率之间的分配。
英文摘要
Previous work has shown that first-order Palatini gravity may be cast as a non-conservative Herglotz Lagrangian field theory, which excludes the conformal mode from its space of dynamical variables. In the present work, we analyse the role of the $SO(1,3)$ gauge connection in the construction of this action-dependent theory. The connection may be algebraically decomposed into complementary sectors which we interpret as `shape' and `scale' components. Only the former is retained within the Herglotz theory, while the latter is incorporated into the action-dependent sector. It is shown that the choice of connection decomposition is a space that can be smoothly parameterised. Such an observation leads to the finding that there exists a `moduli space of frictional field theories', in which each point corresponds to a distinct algebraic splitting of the connection into shape and scale pieces. Movement within the moduli space transitions between Herglotz Lagrangians whose on-shell dynamics all reproduce first-order Palatini gravity. The distinction lies in how the reproduction of the scale dynamics of the original theory is partitioned between action dependence and dynamical torsion.
发表机构
- Lancaster University（兰卡斯特大学）
机构由 AI 辅助整理，请以论文原文为准。
