On magnetic monopole and Dirac quantization condition in the minimal length formalism

In this article, we study the effects of minimal length corrections on the cyclotron acceleration and radiation of a charged particle moving in a magnetic monopole field. Using the modified Hamiltonian describing the dynamics of a charged particle moving in a magnetic monopole field we derive the modified cyclotron frequency and modified acceleration. Also, we derive the modified power for the cyclotron radiation using the modified acceleration. We find that all modified quantities are dependent of the deformation parameter α . In addition, we find that, the modified electromagnetic angular momentum and magnetic charges are not quantized as an integer multiple, thus we establish the modified Dirac quantization condition and the usual Dirac quantization condition is just the term of zero order in α . The modified Dirac quantization condition allows fractional charges which arise from vacuum fluctuations. In the Born approximation, we derive the modified scattering cross section and then we estimate the upper bound on the minimal length.