Conformal symmetry and constants of motion

Conformal space-time symmetries of electromagnetic fields and potentials are studied in order to determine whole sets of constants of motion when spin- 1/2 charged particles interact with such external electromagnetic fields. The relativistic and nonrelativistic contexts are discussed through the Hamiltonian formalism. In particular, the interesting example of the magnetic monopole field is recovered and related to the recent works of Jackiw and D’Hoker–Vinet.