Magnetic monopoles are hypothetical particles consisting of an isolated north or south magnetic pole without a partner. Though they are currently unobserved, predictions from quantum field theory indicate that if they do exist, they should be produced in north-south pairs by a strong enough magnetic field.

The rate of production of monopoles in weak, constant magnetic fields has been known for decades, but strong fields and fields that change in space and time present significant complications. This thesis calculates the rate of monopole production in time-dependent fields, and in constant fields well beyond the weak-field limit. We find that in field theories admitting monopoles as topological solitons, such as Grand Unified Theories, monopole production occurs by a classical instability when the field exceeds the Ambjørn-Olesen critical field strength. In doing this, we explicitly compute new sphaleron and instanton solutions in Georgi-Glashow SU(2) theory for the first time. The techniques we use to find these solutions are applicable beyond monopole production---we also compute the electroweak sphaleron configuration, responsible for baryon and lepton number violation in the Standard Model, in the background of a strong magnetic field, over the full range of physically relevant field strengths.

Our calculations are motivated by the possibility of producing monopoles in ultrarelativistic heavy ion collisions, which generate some of the strongest magnetic fields in the known Universe. Though a complete calculation of the monopole production cross section in these collisions remains elusive, we present approximations that can reasonably be expected to give a lower bound on the overall production probability, and compute the approximate momentum distribution of the produced particles. This information can be used directly by experimental collaborations to place bounds on monopole masses using data from heavy ion collisions.