Dimensionless physics: continuation

Several approaches to quantum gravity (including the model of superplastic vacuum; Diakonov tetrads emerging as the bilinear combinations of the fermionis fields; $BF$-theories of gravity; and effective acoustic metric) suggest that in general relativity the metric must have dimension 2, i.e. $[g_{\mu \nu }]=1\mathrm{/}[L{]}^2$, irrespective of the dimension of spacetime. This leads to the “dimensionless physics” discussed in the review paper G.E. Volovik, Dimensionless physics, JETP 132, 727 (2021). Here we continue to exploit this unusual dimension of the metric.