  A Dirac electron field is quantized in the background of a Dirac magnetic
monopole, and the phenomenon of induced quantum numbers in this system is
analyzed. We show that, in addition to electric charge, also squares of orbital
angular momentum, spin, and total angular momentum are induced. The functional
dependence of these quantities on the temperature and the CP-violating vacuum
angle is determined. Thermal quadratic fluctuations of charge and squared total
angular momentum, as well as the correlation between them and their
correlations with squared orbital angular momentum and squared spin, are
examined. We find the conditions when charge and squared total angular momentum
at zero temperature are sharp quantum observables rather than mere quantum
averages.
