Abstract:
In this thesis, we have studied the methods of Resurgence and Pad\'{e}-Borel reconstruction for the one-field Euler-Heisenberg Lagrangian in the context of scalar quantum electrodynamics upto the order of one and two loops, and for the two-field Euler-Heisenberg Lagrangian in the context of quantum electrodynamics upto one loop. Both of these applications of Pad\'{e}-Borel reconstructions have been largely unexamined in literature. We have derived the form of the two-field Euler-Heisenberg Lagrangian for sQED from first principles upto the order of two loops. By the means of Pad\'{e}-Borel reconstruction strategies, we have constructed remarkably accurate functional approximations to the Euler-Heisenberg Lagrangian using very limited amount of perturbative data. We have been able to predict the behaviour of this function in the non-perturbative strong field regime using these approximations and other methods developed in the program of Resurgence. In our analysis, we have drawn parallels between our work and the literature already present on this subject in the case of the quantum electrodynamics Euler-Heisenberg Lagrangian, as well as pointed out new resurgent structures that had not been studied extensively in the literature.
