论文标题
无量纲的物理学
Dimensionless physics
论文作者
论文摘要
我们讨论了紧急引力的两种情况。在其中一个中，量子真空被认为是巨型晶体，有效的重力描述了该晶体的动态弹性变形。在另一个中，引力四元素作为费米原场的双线性形式出现。尽管本质上具有重力的本质不同的机制，但这两种情况具有一个重要的共同特性：度量场具有长度$ [g_ {μL] = 1/[l]^2 $的反向平方的尺寸，与常规尺寸无尺寸指标不同，$ [g_ {μ{μ= 1 $ $，在一般情况下。结果，遵守差异不变的物理量变得无限。这发生在牛顿常数，标量曲率，宇宙常数，颗粒质量，费米子和标量骨磁场等等数量上。这可能表明无量纲的物理可以是差异不变性的自然结果，因此可以是任何重力的一般性质，在量子真空中出现。维度转移的非平凡后果之一与拓扑有关。由于尺寸的变化，一些操作员变为拓扑，并在动作中包含整数或分数预成分。这特别涉及固有的3+1量子霍尔效应和Nieh-Yan量子异常在扭转方面。
We discuss two scenarios of emergent gravity. In one of them the quantum vacuum is considered as superplastic crystal, and the effective gravity describes the dynamical elastic deformations of this crystal. In the other one the gravitational tetrads emerge as the bilinear form of the fermionic fields. In spite of the essentially different mechanisms of emergent gravity, these two scenarios have one important common property: the metric field has dimension of the inverse square of length $[g_{μν}]=1/[l]^2$, as distinct from the conventional dimensionless metric, $[g_{μν}]=1$, in general relativity. As a result the physical quantities, which obey diffeomorphism invariance, become dimensionless. This takes place for such quantities as Newton constant, the scalar curvature, the cosmological constant, particle masses, fermionic and scalar bosonic fields, etc. This may suggest that the dimensionless physics can be the natural consequence of the diffeomorphism invariance, and thus can be the general property of any gravity, which emerges in the quantum vacuum. One of the nontrivial consequences of the shift of dimensions is related to topology. Due to the shift of dimensions some operators become topological, and contain the integer or fractional prefactors in the action. This in particular concerns the intrinsic 3+1 quantum Hall effect and the Nieh-Yan quantum anomaly in terms of torsion.
