Superintegrable relativistic systems in scalar background fields

@article{Ansell2018SuperintegrableRS,
  title={Superintegrable relativistic systems in scalar background fields},
  author={Lauren Elizabeth Ansell and Tom Heinzl and Anton Ilderton},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2018},
  volume={51}
}
We consider a relativistic charged particle in a background scalar field depending on both space and time. Poincaré, dilation and special conformal symmetries of the field generate conserved quantities in the charge motion, and we exploit this to generate examples of superintegrable relativistic systems. We also show that the corresponding single-particle wavefunctions needed for the quantum scattering problem can be found exactly, by solving the Klein–Gordon equation. 
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