# Klein–Gordon Oscillator in a Topologically Nontrivial Space-Time

Santos, L. C. N.  (Departamento de Física, CFM, Universidade Federal de Santa Catarina, CP 476, 88.040-900 Florianópolis, SC, Brazil) ; Mota, C. E. (Departamento de Física, CFM, Universidade Federal de Santa Catarina, CP 476, 88.040-900 Florianópolis, SC, Brazil) ; Barros, C. C. (Departamento de Física, CFM, Universidade Federal de Santa Catarina, CP 476, 88.040-900 Florianópolis, SC, Brazil)

13 May 2019

Abstract: In this study, we analyze solutions of the wave equation for scalar particles in a space-time with nontrivial topology. Solutions for the Klein–Gordon oscillator are found considering two configurations of this space-time. In the first one, the ${S}^{\mathrm{1}}×{R}^{\mathrm{3}}$ space is assumed where the metric is written in the usual inertial frame of reference. In the second case, we consider a rotating reference frame adapted to the circle ${S}^{\mathrm{1}}$ . We obtained compact expressions for the energy spectrum and for the particles wave functions in both configurations. Additionally, we show that the energy spectrum of the solution associated with the rotating system has an additional term that breaks the symmetry around $E=\mathrm{0}$ .

Published in: Advances in High Energy Physics 2019 (2019) 2729352