论文标题
非金属几何形状作为规模不变理论中质量的起源
Non-metric geometry as the origin of mass in gauge theories of scale invariance
论文作者
论文摘要
我们讨论了标准模型（SM）和爱因斯坦重力之外的规模不变性理论。测量这种对称性的结果是它们的基础4D几何形状是非金属的（$ \nabla_μg_{αβ} \ not = 0 $）。这种理论的例子是weyl的{\ it原始}二次引力理论及其palatini版本。这些理论具有与爱因斯坦重力对称的测量量表对称性的自发断裂。所有质量量表都有几何起源：普朗克量表（$ m_p $），宇宙常数（$λ$）和weyl量规玻色子（$ω_μ$）的质量对称性的质量与标量场vev成正比，该标量场vev与（几何）$ \ tilde r^2 $ term in Action中具有起源。 SM Higgs字段具有$ω__$的非金属几何来源，也具有相似的起源，由Weyl Boson Fusion在早期宇宙中产生。这似乎是对应用于宇宙学的开放系统的热力学中讨论的“物质创造”的微观实现。 Unlike in local scale invariant theories (no $ω_μ$ present) with an underlying pseudo-Riemannian geometry, in our case: 1) there are no ghosts and no additional fields beyond the SM and underlying Weyl or Palatini geometry, 2) the cosmological constant is positive and is small because gravity is weak, 3) the Weyl or Palatini connection shares the Weyl (gauge) symmetry of the action,和：4）存在该对称性的非平凡，保守的Weyl电流。从固态物理学的角度来看，也提供了非金属性及其与质量产生关系的直观图片，它是常见的，并且与晶体结构的点缺陷（度量异常）相关。
We discuss gauge theories of scale invariance beyond the Standard Model (SM) and Einstein gravity. A consequence of gauging this symmetry is that their underlying 4D geometry is non-metric ($\nabla_μg_{αβ}\not=0$). Examples of such theories are Weyl's {\it original} quadratic gravity theory and its Palatini version. These theories have spontaneous breaking of the gauged scale symmetry to Einstein gravity. All mass scales have a geometric origin: the Planck scale ($M_p$), cosmological constant ($Λ$) and the mass of the Weyl gauge boson ($ω_μ$) of scale symmetry are proportional to a scalar field vev that has an origin in the (geometric) $\tilde R^2$ term in the action. With $ω_μ$ of non-metric geometry origin, the SM Higgs field also has a similar origin, generated by Weyl boson fusion in the early Universe. This appears as a microscopic realisation of "matter creation from geometry" discussed in the thermodynamics of open systems applied to cosmology. Unlike in local scale invariant theories (no $ω_μ$ present) with an underlying pseudo-Riemannian geometry, in our case: 1) there are no ghosts and no additional fields beyond the SM and underlying Weyl or Palatini geometry, 2) the cosmological constant is positive and is small because gravity is weak, 3) the Weyl or Palatini connection shares the Weyl (gauge) symmetry of the action, and: 4) there exists a non-trivial, conserved Weyl current of this symmetry. An intuitive picture of non-metricity and its relation to mass generation is also provided from a solid state physics perspective where it is common and is associated with point defects (metric anomalies) of the crystalline structure.
