Schwinger pair production in SL (2, C) topologically nontrivial fields via non-Abelian worldline instantons

Schwinger pair production is analyzed in a Belavin, Polyakov, Schwarz and Tyupkin (BPST) instanton background and in its SL(2, C) complex extension for complex scalar particles. A non-Abelian extension of the worldline instanton method is utilized, wherein Wong's equations in a coherent state picture adopted for SL(2, C) are solved in Euclidean spacetime. While pair production is not predicted in the BPST instanton, a complex extension of the BPST instanton, existing as parallel fields in Minkowski spacetime, is shown to decay via the Schwinger effect.