Non-Euclidean geometry, nontrivial topology and quantum vacuum effects
arXiv:1711.00450 · doi:10.3390/universe4020023
Abstract
Space out of a topological defect of the Abrikosov-Nielsen-Olesen vortex type is locally flat but non-Euclidean. If a spinor field is quantized in such a space, then a variety of quantum effects is induced in the vacuum. Basing on the continuum model for long-wavelength electronic excitations, originating in the tight-binding approximation for the nearest neighbor interaction of atoms in the crystal lattice, we consider quantum ground state effects in monolayer structures warped into nanocones by a disclination; the nonzero size of the disclination is taken into account, and a boundary condition at the edge of the disclination is chosen to ensure self-adjointness of the Dirac-Weyl Hamiltonian operator. In the case of carbon nanocones, we find circumstances when the quantum ground state effects are independent of the boundary parameter and the disclination size.
13 pages, minor changes, misprints eliminated