Violação espontânea da simetria de Lorentz, não-comutatividade e cenário de Kaluza-Klein para uma partícula escalar relativística

Abstract

In this work we initially investigate an anisotropic space scenario generated by a term from a spontaneous break in Lorentz symmetry and allows an extension of the standard model. Another possibility of violation of this type appears in non-commutative theories, also promoting a deformed Heisenberg algebra associated with a minimum length. Next, we analyze three cases for a relativistic scalar particle in a Kaluza-klein theory scenario. In the rst case, we analyze the Aharonov-Bohm e ect for linked states, where the particle was subject to a Coulomb-type potential. In a second scenario, the particle is subject to the Klein-Gordon oscillator and to a Cornell-type potential. We obtain analytically the energy spectrum for the particle in this case and for the particular cases, where the particle is inuenced by a Coulomb-type potential and then by a linear potential. In the latter case, we study a particle in a non-inertial frame, but initially it is not found in a Kaluza-Klein theory. In a particular case, the particle is in a region limited by cylindrical surfaces. In addition, we have the case of the position-dependent particle interacting with a Coulomb-type potential. And, nally, we deal with the Klein-Gordon oscillator, in a rotating reference frame in Kaluza-Klein space-time.