发表机构
HUN-REN Wigner Research Centre for Physics（HUN-REN维格纳物理研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在拉格朗日场论框架下，系统构造了线性化引力中与洛伦兹、膨胀及特殊共形变换相关的守恒流，补充了角动量张量、膨胀流和特殊共形张量，并推广了诺特定理以处理规范固定条件，推导了多参数族及局部平衡方程。
AI 中文摘要
在闵可夫斯基背景下，我们扩展了先前关于线性化引力场能量-动量张量的工作，在拉格朗日场论框架内，探讨了与洛伦兹变换、膨胀变换和特殊共形变换相关的线性化引力中的守恒流。我们既考虑了突出的特殊情况，也考虑了一般参数族流。对于前者，我们先前基于线性化引力与电动力学之间的相似性发现的独特能量-动量张量 $T_{\mathrm{lg}}^{ab}$，现在补充了与洛伦兹对称性和膨胀对称性相关的角动量张量 $M_{\mathrm{lg}}^{abc}$ 和膨胀流 $D_{\mathrm{lg}}^a$。关于特殊共形变换，我们提出了一种诺特定理的推广，该推广在施加额外条件（如规范固定条件）时很有用；我们证明了在广义调和规范下，特殊共形变换是线性化引力的诺特对称性，并利用广义诺特定理得到了伴随 $T_{\mathrm{lg}}^{ab}$ 的特殊共形张量 $C_{\mathrm{lg}}^{ab}$。我们还讨论了伴随另外两个显著能量-动量张量的角动量张量、膨胀流和特殊共形张量。我们还确定了伴随一般能量-动量张量族（该族先前已发现，包括正则能量-动量张量）的一般多参数族 $M^{abc}$、$D^a$ 和 $C^{ab}$ 张量，并推导了它们在存在物质时相关的局部平衡方程。它们的成员不依赖于线性化度规的一阶以上导数。
英文摘要
Extending a previous work on the energy-momentum tensor of the linearized gravitational field in Minkowski background, conserved currents in linearized gravity associated with Lorentz transformations, dilatations and special conformal transformations are explored in the framework of Lagrangian field theory. Both outstanding special cases and general parametric families of currents are considered. Regarding the former, the distinguished energy-momentum tensor $T_{\mathrm{lg}}^{ab}$ we found earlier, guided by similarities between linearized gravity and electrodynamics, is supplemented with an angular momentum tensor $M_{\mathrm{lg}}^{abc}$ and a dilatation current $D_{\mathrm{lg}}^a$, associated with Lorentz and dilatation symmetries. Concerning special conformal transformations, a generalization of Noether's theorem that is useful if additional conditions (such as gauge fixing conditions) are imposed is formulated, it is shown that special conformal transformations are Noether symmetries of linearized gravity in the generalized harmonic gauges, and a special conformal tensor $C_{\mathrm{lg}}^{ab}$, accompanying $T_{\mathrm{lg}}^{ab}$, is obtained using the generalized Noether's theorem. The angular momentum tensor, dilatation current and special conformal tensor accompanying two other notable energy-momentum tensors are discussed as well. General multi-parameter families of $M^{abc}$, $D^a$ and $C^{ab}$ tensors accompanying a general family of energy-momentum tensors, which was found earlier and includes canonical energy-momentum tensors, are also determined, and local balance equations that are relevant if matter is present are derived for them. Their members do not depend on higher than first derivatives of the linearized metric.
Comments62 pages
