Resurgent transseries $\&$ Dyson-Schwinger equations

Understand

We employ resurgent transseries as algebraic tools to investigate two self-consistent Dyson-Schwinger equations, one in Yukawa theory and one in quantum electrodynamics.

• After a brief but pedagogical review, we derive fixed point equations for the associated anomalous dimensions and insert a moderately generic log-free transseries ansatz to study the possible strictures imposed.
• While proceeding in various stages, we develop an algebraic method to keep track of the transseries' coefficients.
• We explore what conditions must be violated in order to stay clear of fixed point theorems to eschew a unique solution, if so desired, as we explain.