Combined Lorentz Symmetry: Lessons from Superfluid 3 He

G. E. Volovik*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
36 Downloads (Pure)


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 3He: the 3He-A scenario and the 3He-B scenario. In these scenarios, the gravitational tetrads are considered as the order parameter of the symmetry breaking in the quantum vacuum. The 3He-B 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 left-handed fermions, the tetrad for the right-handed 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 languageEnglish
Pages (from-to)1-15
Number of pages15
JournalJournal of Low Temperature Physics
Issue number1-2
Early online date29 Oct 2021
Publication statusPublished - Jan 2022
MoE publication typeA1 Journal article-refereed


  • Lorentz symmetry
  • Symmetry breaking
  • Topological superfluid


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