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Abstract: We discuss phenomenology of quantum vacuum. Phenomenology of macroscopicsystems has three sources: thermodynamics, topology and symmetry.Thermodynamics of the self-sustained vacuum allows us to treat the problemsrelated to the vacuum energy: the cosmological constant problems. The naturalvalue of the energy density of the equilibrium the self-sustained vacuum iszero. Cosmology is discussed as the process of relaxation of vacuum towards theequilibrium state. The present value of the cosmological constant is very smallcompared to the Planck scale, because the present Universe is very old and thusis close to equilibrium. Momentum space topology determines the universalityclasses of fermionic vacua. The Standard Model vacuum both in its massless andmassive states is topological medium. The vacuum in its massless state sharesthe properties of superfluid 3He-A, which is topological superfluid. It belongsto the Fermi-point universality class, which has topologically protectedfermionic quasiparticles. At low energy they behave as relativistic masslessWeyl fermions. Gauge fields and gravity emerge together with Weyl fermions atlow energy. This allows us to treat the hierarchy problem in Standard Model:the masses of elementary particles are very small compared to the Planck scalebecause the natural value of the quark and lepton masses is zero. The smallnonzero masses appear in the infrared region, where the quantum vacuum acquiresthe properties of another topological superfluid, 3He-B, and 3+1 topologicalinsulators. The other topological media in dimensions 2+1 and 3+1 are alsodiscussed. In most cases, topology is supported by discrete symmetry of theunderlying microscopic system, which indicates the important role of discretesymmetry in Standard Model.

Autor: G.E. Volovik


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