局部单位不变性、反作用牵引子和宇宙学常数问题
Local Unit Invariance, Back-Reacting Tractors and the Cosmological Constant Problem
摘要：
当物理学以一种与单位系统的局部选择无关的方式表达时，黎曼几何就被共形几何所取代。此外，质量变成几何的，表现为外尔权的拖拉机（共形多重场必须保持局部单位不变性的表现）。这些权重和质量之间的关系是通过标量曲率来实现的。因此，质量项对于离壳引力背景是时空相关的，但对于物理的爱因斯坦流形是恒定的。不幸的是，这引入了一个自然性问题，因为标量曲率与宇宙学常数成正比。通过写下牵引应力张量（从标准应力张量及其一阶和二阶导数构建的多重态），我们展示了反作用如何解决这个自然性问题。我们还表明，经典的反作用产生一个有趣的标量场的潜力。我们推测，对物理系统如何与尺度耦合的适当描述，可以提高我们对粒子物理与观测到的宇宙学常数之间的差异所引起的自然性问题的理解。我们进一步给出了一些想法如何环境描述的拖拉机演算可能会导致一个Ricci平坦/CFT对应推广的AdS侧Maldacena的对偶性的Ricci平坦空间的一个更高的维度。
英文摘要：
When physics is expressed in a way that is independent of local choices of unit systems, Riemannian geometry is replaced by conformal geometry. Moreover masses become geometric, appearing as Weyl weights of tractors (conformal multiplets of fields necessary to keep local unit invariance manifest). The relationship between these weights and masses is through the scalar curvature. As a consequence mass terms are spacetime dependent for off-shell gravitational backgrounds, but happily constant for physical, Einstein manifolds. Unfortunately this introduces a naturalness problem because the scalar curvature is proportional to the cosmological constant. By writing down tractor stress tensors (multiplets built from the standard stress tensor and its first and second derivatives), we show how back-reaction solves this naturalness problem. We also show that classical back-reaction generates an interesting potential for scalar fields. We speculate that a proper description of how physical systems couple to scale, could improve our understanding of naturalness problems caused by the disparity between the particle physics and observed, cosmological constants. We further give some ideas how an ambient description of tractor calculus could lead to a Ricci-flat/CFT correspondence which generalizes the AdS side of Maldacena's duality to a Ricci-flat space of one higher dimension.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
