Topology, thermodynamics and dynamics of quantum vacuum in effective theory

G.E. Volovik

The new paradigm in modern physics suggests that the Standard Model (SM) of elementary particle physics and the Einsten general relativity are both the effective theories.

In one scenario, they both emerge at low energy from the still unknown microscopic structure of the quantum vacuum as a natural consequence of topology of Green's function in momentum space. Close to the Green's function singularity, the low-energy fermionic excitations behave as relativistic Weyl fermions - the bricks from which all elementary particles of SM are constructed. The bosonic collective modes in such system behave as gauge and gravitational fields, which interact with fermionic excitations. Such behavior is generic and does not depend on the details of the microscopic structure of the quantum vacuum, provided that it belongs to the Fermi point universality class. In principle, all the ingredients of the SM may emerge near the Fermi points.

Irrespective of the scenario of emergence of the effective gravity, there is a general thermodynamic approach which is applicable to any quantum vacuum. Among the other things it may suggest the possible solution of the cosmological constant problem, if the quantum vacuum belongs to the class of self-sustained systems. In such a system, the large (Planck scale) zero point energy is automatically cancelled by the contribution of microscopic degrees of freedom of the vacuum without fine-tuning, if the vacuum is in thermodynamic equilibrium. The dynamics of the self-sustained relativistic vacuum demonstrates how the initially huge energy of non-equilibrium vacuum may relax to zero in equilibrium or to its present small value.