Classification of Emergent Weyl Spinors in Multi-Fermion Systems

Zubkov, M. A.

doi:10.1134/s0021364021070031

Cited by 7 publications

(6 citation statements)

References 43 publications

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“…When the gravitational tetrads are taken into account, the discrete P T symmetry of spacetime acquires new formulations, since the sign of the tetrad field becomes also important. [3][4][5][6][7] In particular, if the tetrads are composite objects, which are formed as bilinear combinations of the fermionic operators, 8-10 the parity P and the time reversal T operations are formed as combinations of the original more fundamental symmetry operators, P = P c P s and T = T c T s . Here P c and T c refer to pure coordinate transformations, P c r = −r and T c t = −t, while P s and T s refer to the corresponding transformations of Dirac or Weyl spinors.…”

Section: Pt Symmetry In Relativistic Quantum Fieldsmentioning

confidence: 99%

A note on the vacuum structure of lattice Euclidean quantum gravity: ‘birth’ of macroscopic space-time and PT-symmetry breaking

Vergeles

2021

Class. Quantum Grav.

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This paper is motivated by the recent paper M. Baldovin, S. Iubini, R. Livi and A. Vulpiani, Statistical mechanics of systems with negative temperature, arXiv:2103.12572. The authors suggest that negative absolute temperatures are consistent with equilibrium thermodynamics. This is correct, if the environment also has negative temperature. Otherwise such states represent the transient though maybe long-lived metastable effects. Here we consider the extension of the negative temperatures to the relativistic systems. We show that the negative state is possible in the Dirac vacuum, which is obtained by the P T symmetry transformation from the conventional Dirac sea. If such vacuum with inverse population fills the whole Universe, its thermodynamics determined by negative temperatures becomes equilibrium.

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Section: Pt Symmetry In Relativistic Quantum Fieldsmentioning

confidence: 99%

A note on the vacuum structure of lattice Euclidean quantum gravity: ‘birth’ of macroscopic space-time and PT-symmetry breaking

Vergeles

2021

Class. Quantum Grav.

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“…The topological invariants for different types of the Weyl points are discussed in Ref. [33,34]. ( In our approach, four tetrads in Eq.…”

Section: Weyl Fermions and Multiple Tetradsmentioning

confidence: 99%

“…[38], it is not excluded that due to the small value of the splitting in Eq. (33), this problem can be avoided. Anyway, the possible scenario of emergent bi-metricity requires the detailed study.…”

Section: Possible Bi-metric Gravity From Multiple Tetradsmentioning

confidence: 99%

Combined Lorentz Symmetry: Lessons from Superfluid $$^3$$He

Volovik

2021

J Low Temp Phys

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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 $$^3$$ 3 He: the $$^3$$ 3 He-A scenario and the $$^3$$ 3 He-B scenario. In these scenarios, the gravitational tetrads are considered as the order parameter of the symmetry breaking in the quantum vacuum. The $$^3$$ 3 He-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.

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“…The more complicated models should take into account the chirality of fermions. 16 The action (2) has the full symmetry G of the microscopic vacuum without gravity. Since the metric is absent, the distance between the spacetime points is not determined, as a result the original vacuum is not sensitive to the coordinate transformations.…”

Section: Model For Symmetric Vacuummentioning

confidence: 99%

Gravity from symmetry breaking phase transition

Volovik

2021

Preprint

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The paper is devoted to the memory of Dmitry Diakonov. We discuss gravity emerging in the fermionic vacuum as suggested by Diakonov 10 years ago in his paper "Towards lattice-regularized Quantum Gravity". 1 Gravity emerges in the phase transition. The order parameter in this transition is the tetrad field, which appears as the bilinear composite of the fermionic fields. This symmetry breaking gives 6 Nambu-Goldstone modes; 6 gauge bosons in the spin-connection fields, which absorb 6 NG modes and become massive gauge bosons; and 6 Higgs fields. The similar scenario of the symmetry breaking with appearance of the 5 + 1 Higgs gravitons takes place in the B-phase of superfluid 3 He. While in 3 He-B these Higgs modes are all massive, in the GR these Higgs collective modes give rise to two massless gravitational waves.

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Classification of Emergent Weyl Spinors in Multi-Fermion Systems

Cited by 7 publications

References 43 publications

A note on the vacuum structure of lattice Euclidean quantum gravity: ‘birth’ of macroscopic space-time and PT-symmetry breaking

A note on the vacuum structure of lattice Euclidean quantum gravity: ‘birth’ of macroscopic space-time and PT-symmetry breaking

Combined Lorentz Symmetry: Lessons from Superfluid $$^3$$He

Gravity from symmetry breaking phase transition

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