作为统一物理学原理的单位不变性
Unit Invariance as a Unifying Principle of Physics
摘要：
物理学的一个基本原则是在描述物理量时可以自由地局部选择任何单位系统。它的实现相当于把外尔不变性当作所有物理理论的基本对称性。在这篇论文中，我们研究了这个“单位不变性”原则的结果，发现它是一个统一的原则。单位不变性是通过引入一个称为标度的规范场来实现的，它被设计用来测量单位系统如何从一点到另一点变化。事实上，通过统一和简单的外尔不变耦合的规模和物质领域，我们统一无质量，大规模，部分无质量的激发。因此，质量决定了物理量对尺度变化的响应。这种响应是由某些“拖拉机外尔重量”校准的。这些权重的现实产生Breitenlohner-Freedman在反德西特空间的稳定性界限。我们的方法的另一个有价值的成果是构造共形不变理论的一般机制。特别是，我们提供了新的外尔不变量Deser-Nepomechie矢量和自旋三分之一理论的直接推导，以及新的更高的自旋概括。为了构建这些理论，采用了来自共形几何的“拖拉机演算”，它在所有阶段都保持明显的外尔不变性。事实上，我们的方法取代了通常的黎曼几何描述的物理与共形几何。在相同的框架内，我们也给出了一个描述的费米子和相互作用的超对称理论，再次统一无质量和大规模的激发。
英文摘要：
A basic principle of physics is the freedom to locally choose any unit system when describing physical quantities. Its implementation amounts to treating Weyl invariance as a fundamental symmetry of all physical theories. In this thesis, we study the consequences of this "unit invariance" principle and find that it is a unifying one. Unit invariance is achieved by introducing a gauge field called the scale, designed to measure how unit systems vary from point to point. In fact, by a uniform and simple Weyl invariant coupling of scale and matter fields, we unify massless, massive, and partially massless excitations. As a consequence, masses now dictate the response of physical quantities to changes of scale. This response is calibrated by certain "tractor Weyl weights". Reality of these weights yield Breitenlohner-Freedman stability bounds in anti de Sitter spaces. Another valuable outcome of our approach is a general mechanism for constructing conformally invariant theories. In particular, we provide direct derivations of the novel Weyl invariant Deser--Nepomechie vector and spin three-half theories as well as new higher spin generalizations thereof. To construct these theories, a "tractor calculus" coming from conformal geometry is employed, which keeps manifest Weyl invariance at all stages. In fact, our approach replaces the usual Riemannian geometry description of physics with a conformal geometry one. Within the same framework, we also give a description of fermionic and interacting supersymmetric theories which again unifies massless and massive excitations.
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。
