2002/02/06 by P. Castelo Ferreira, Ferreira, P. Castelo
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Mechanics and Applications #Quantum, superfluid, helium dynamics #Topological Materials and Phenomena #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0202033
v3: 1+15 pages, 5 figures; current version with journal. Units corrected. White-hole properties studied, using Moyal-Weyl quantization it is shown that the wave function vanishes at the horizon
openalex publication_date 2002/02/06 · arxiv created 2006/02/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is built a map between an Abelian Topological Quantum Field Theory, 2+1D compact U(1) gauge Maxwell Chern-Simons Theory and the nonrelativistic quantum mechanics Azbel-Hofstadter model of Bloch electrons. The Uq(sl2) quantum group and the magnetic translations group of the Azbel-Hofstadter model correspond to discretized subgroups of U(1) with linear gauge parameters. The magnetic monopole confining and condensate phases in the Topological Quantum Field Theory are identified with the extended (energy bands) and localized (gaps) phases of the Bloch electron. The magnetic monopole condensate is associated, at the nonrelativistic level, with gravitational white holes due to deformed classical gauge fields. These gravitational solutions render the existence of finite energy pure magnetic monopoles possible. This mechanism constitutes a dynamical symmetry breaking which regularizes the solutions on those localized phases allowing physical solutions of the Shrödinger equation which are chains of electron filaments connecting several monopole-white holes.To test these results would be necessary a strong external magnetic field B∼ 5 T at low temperature T<1 K. To be accomplished, it would test the existence of magnetic monopoles and classical gravity to a scale of ∼ 10-15 meters, the dimension of the monopole-white hole. A proper discussion of such experiment is out of the scope of this theoretical work.