  The imaginary part of the one loop effective action in external backgrounds
can be efficiently computed using worldline instantons which are closed
periodic paths in spacetime. Exact solutions for nonstatic backgrounds are only
known in certain cases. In this paper, we propose a novel technique allowing
the construction of further exactly solvable models. In order to do so, we
introduce a deformation function which maps the worldline instantons for a
given model to the closed periodic stationary paths of a new model. Executing
this procedure iteratively results in a chain of infinitely many solvable
models. Similar ideas were applied to topological and nontopological defects in
quantum field theory. We explicitly discuss the tunneling exponential in the
Schwinger pair creation rate and illustrate the validity of the proposed
technique for well-known cases.
