Amelino-Camelia DSR effects on scalar fields in static cosmic string spacetime

We investigate the impact of Amelino-Camelia Doubly Special Relativity (DSR) on Klein-Gordon (KG) scalar particles in a (2+1)-dimensional spacetime containing a static cosmic string. By incorporating Lorentz-scalar and non-minimal couplings under a uniform magnetic field, we derive a wave equation incorporating leading-order Planck-scale effects, yielding closed-form energy spectra that generalize the relativistic Landau levels and reveal DSR-induced energy splittings between particle and antiparticle states arising from shifts in the cyclotron frequency rather than rest-mass energy (ε o ) differences. The corresponding quantum states can manifest as rotating magnetic vortex modes, further modulated by the nontrivial spacetime topology. Extending the model to include a linear non-minimal coupling, which introduces a KG oscillator, we observe enhanced energy splittings that reduce to the magnetic-only scenario in the appropriate limit. Introducing a Coulomb-type Lorentz-scalar potential allows computation of first-order contributions to the binding energies proportional to ε o /ε p , producing deviations from the classical Coulomb spectrum, with quantum states emerging as either static ring-like or rotating vortex-like modes strongly influenced by the cosmic string geometry and the repulsive centrifugal barrier. This analysis provides a comprehensive theoretical characterization of leading-order Planck-scale effects and topological defects on relativistic quantum states, although these effects remain exceedingly small at experimentally accessible energies and lie beyond current detection capabilities.