Dirac magnetic monopole and the discrete symmetries

We examine several issues related to the processes of Dirac monopole-antimonopole production in high-energy collisions such as $e^+e^-$ annihilation. Perturbative calculations for such processes are known to be inherently ambiguous due to the arbitrariness of direction of the monopole string; this requires use of some prescription to obtain physical results. We argue that different prescriptions lead to drastically different physical results which suggests that at present we do not have an entirely satisfactory procedure for the elimination of string arbitrariness (this problem is quite separate from the problems caused by the large coupling constant). We then analyze the consequencies of discrete symmetries (P and C) for the monopole production processes and for the monopole-antimonopole states. The P and C selection rules for the monopole-antimonopole states turn out to be different from those for the ordinary fermion-antifermion or boson-antiboson system. In particular, the spin 1/2 monopole and antimonopole should have the same helicities if they are produced through the one-photon annihilation of an electron and positron. A stronger selection rule holds for spinless monopoles: CP symmetry absolutely forbids the monopole-antimonopole production through the one-photon annihilation of an electron and positron. Single-photon $e^+e^- \to g^+g^-$ amplitude has been a key input in calculating the contribution of virtual $g^+g^-$ pairs to various physical processes such as the decay $Z\to 3\gamma$ and the anomalous magnetic moment of the electron. Applying our conclusions to these cases can lead to significant modifications of the results obtained in previous works.