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Abstract
We consider the possibility of the scenario in which the P, T and Lorentz symmetry of the relativistic quantum vacuum are all the combined symmetries. These symmetries emerge as a result of the symmetry breaking of the more fundamental P, T and Lorentz symmetries of the original vacuum, which is invariant under separate groups of the coordinate transformations and spin rotations. The condensed matter vacua (ground states) suggest two possible scenarios of the origin of the combined Lorentz symmetry, and both are realized in the superfluid phases of liquid ^{3}He: the ^{3}HeA scenario and the ^{3}HeB scenario. In these scenarios, the gravitational tetrads are considered as the order parameter of the symmetry breaking in the quantum vacuum. The ^{3}HeB scenarios applied to the Minkowski vacuum lead to the continuous degeneracy of the Minkowski vacuum with respect to the O(3, 1) spin rotations. The symmetry breaking leads to the corresponding topological objects, which appear due to the nontrivial topology of the manifold of the degenerate Minkowski vacua, such as torsion strings. The fourfold degeneracy of the Minkowski vacuum with respect to discrete P and T symmetries suggests that the Weyl fermions are described by four different tetrad fields: the tetrad for the lefthanded fermions, the tetrad for the righthanded fermions, and the tetrads for their antiparticles. This may lead to the gravity with several metric fields, so that the parity violation may lead to the breaking of equivalence principle. Finally, we considered the application of the gravitational tetrads for the solution of the cosmological constant problem.
Original language  English 

Pages (fromto)  115 
Number of pages  15 
Journal  Journal of Low Temperature Physics 
Volume  206 
Issue number  12 
Early online date  29 Oct 2021 
DOIs  
Publication status  Published  Jan 2022 
MoE publication type  A1 Journal articlerefereed 
Keywords
 Lorentz symmetry
 Symmetry breaking
 Topological superfluid
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 1 Finished

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