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Abstract
Diakonov theory of quantum gravity, in which tetrads emerge as the bilinear combinations of the fermionic fields, suggests that in general relativity the metric may have dimension 2; i.e., [g_{uv}=1/[L]^{2}. Several other approaches to quantum gravity, including the model of superplastic vacuum and BFtheories of gravity support this suggestion. 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 (Formula Presented.) is the parameter of the Minkowski metric. The Minkowski parameter (Formula Presented.) is invariant only under Lorentz transformations, and is not diffeomorphism invariant. As a result, the Planck constant (Formula Presented.) has the dimension of length. 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 (Formula Presented.) Then in the thermal contact between the two vacua their temperatures obey the analog of the Tolman law: (Formula Presented.).
Original language  English 

Pages (fromto)  240244 
Number of pages  5 
Journal  JETP Letters 
Volume  117 
Issue number  3 
DOIs  
Publication status  Published  Feb 2023 
MoE publication type  A1 Journal articlerefereed 
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 1 Finished

TOPVAC: From Topological Matter to Relativistic Quantum Vacuum
Volovik, G. (Principal investigator), Nissinen, J. (Project Member), Eltsov, V. (Project Member), Rysti, J. (Project Member), Rantanen, R. (Project Member), Mäkinen, J. (Project Member), Zhang, K. (Project Member), Volard, M.M. (Project Member), Kamppinen, T. (Project Member) & Ikäheimo, A. (Project Member)
01/10/2016 → 30/09/2022
Project: EU: ERC grants