Monopole catalysis of proton decay

The theoretical studies of the monopole catalysis of proton decay in grand unified theories are reviewed. Monopole catalysis, i.e. the ability of magnetic monopoles to induce nucleon decay at a strong interaction rate, is a non-perturbative quantum field theory phenomenon that incorporates the effects of the triangle anomaly and complex structure of the gauge theory vacuum and peculiar properties of fermions in the field of a monopole. This effect is of interest for experiment and astrophysics. By studying the properties of the Dirac equation in the background monopole field reveals that quantum mechanics fails in describing the fermion-monopole interactions. The quantum field theoretic treatment is possible within the s-wave approximation where only spherically symmetric fields are considered. The author reviews various techniques and results of the s-wave theory taking a toy SU(2) model and a realistic SU(5) grand unified theory as examples. He also discusses the corrections to the s-wave approximation and the model dependence of the catalysis.