论文标题
无量纲物理：普朗克常数是Minkowski度量的元素
Dimensionless physics: Planck constant as an element of Minkowski metric
论文作者
论文摘要
diakonov的量子重力理论，其中四元素作为fermionis磁场的双线性组合出现，\ cite {diakonov2011}表明，总体相对论可能具有尺寸2，即$ [g_ {μnν}] = 1/[l] = 1/[l]^2 $。其他几种量子重力的方法，包括超代级真空和$ bf $的模型 - 重力理解支持此建议。这种度量维度的重要结果是，对于时空的任何维度，所有差异不变的数量都是无尺寸的。其中包括操作$ s $，Interval $ s $，宇宙常数$λ$，标量曲率$ r $，标量场$φ$等。在这里，我们正在尝试进一步利用Diakonov的想法，并考虑Planck常数的维度。 Diakonov理论的应用表明，普朗克常数$ \ hbar $是Minkowski Metric的参数。 Minkowski参数$ \ hbar $仅在Lorentz转换下是不变的，并且不是不变的。结果，普朗克常数$ \ hbar $具有非零尺寸 - 长度[l]的尺寸。这个普朗克恒定长度是否与普朗克长度尺度有关，这是一个悬而未决的问题。原则上，可以有不同的Minkowski真空吸尘器，并具有自己的参数$ \ hbar $的值。然后，在两个真空之间的热接触中，它们的温度遵守Tolman定律的类似物：$ \ hbar_1/t_1 = \ hbar_2/t_2 $。
Diakonov theory of quantum gravity, in which tetrads emerge as the bilinear combinations of the fermionis fields,\cite{Diakonov2011} suggests that in general relativity the metric may have dimension 2, i.e. $[g_{μν}]=1/[L]^2$. Several other approaches to quantum gravity, including the model of superplastic vacuum and $BF$-theories of gravity support this suggesuion. The important consequence of such metric dimension is that all the diffeomorphism invariant quantities are dimensionless for any dimension of spacetime. These include the action $S$, interval $s$, cosmological constant $Λ$, scalar curvature $R$, scalar field $Φ$, etc. Here we are trying to further exploit the Diakonov idea, and consider the dimension of the Planck constant. The application of the Diakonov theory suggests that the Planck constant $\hbar$ is the parameter of the Minkowski metric. The Minkowski parameter $\hbar$ is invariant only under Lorentz transformations, and is not diffeomorphism invariant. As a result the Planck constant $\hbar$ has nonzero dimension -- the dimension of length [L]. Whether this Planck constant length is related to the Planck length scale, is an open question. In principle there can be different Minkowski vacua with their own values of the parameter $\hbar$. Then in the thermal contact between the two vacua their temperatures obey the analog of the Tolman law: $\hbar_1/T_1= \hbar_2/T_2$.
