  Schwinger pair production is analyzed in a BPST instanton background and in
its SL$(2,\mathbb{C})$ 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$(2,\mathbb{C})$ 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.
