Testing Lorentz and CPT Symmetries with charged particles

Lorentz and CPT symmetries are foundational symmetries of our current best theories describing nature. The two symmetries state that the laws of physics are invariant under Lorentz transformation or combined transformations of charge conjugation (C), parity inversion (P), and time reversal (T). However, tiny violations of these symmetries could occur in a more fundamental theory. This project investigated possible signals for Lorentz and CPT violation arising from experiments on charged particles in a storage ring. We started with the Dirac equation for a uniform magnetic field and radially outward electric field, and obtained an approximated solution. We then extracted operators for Lorentz and CPT violation from the Standard-Model Extension framework and applied perturbation theory to derive the energy modifications for spin-up and spin-down particles due to Lorentz and CPT violation. Finally, the contributions to the spin precession frequency of a charged particle were obtained by taking the energy differences between different spin states.