Strong-field resummed heat kernels and effective actions: inhomogeneous fields

TL;DR

The paper develops a heat-kernel based framework to achieve resummed expressions for effective actions in strong-background fields, focusing on a quantum scalar coupled to a vector field and extending to a non-gauge derivative coupling. For Abelian backgrounds, it constructs a resummed heat kernel $K_{EM}$ whose coincidence-limit coefficients depend only on field-strength chains, yielding a local Euler–Heisenberg-type prefactor with derivative corrections and clarifying inhomogeneous-field pair creation via the proper-time structure. It then generalizes the approach to a non-gauge vector background, showing that the invariant $N^2$ can be resummed without introducing $N^2$-chains in the generalized Gilkey–Seeley–DeWitt coefficients $a_j^{(N)}$, and provides explicit low-order coefficients to illustrate the pattern. The work points to broad applicability of resummed heat-kernel methods, including curved spacetimes and covariant derivative expansions, with potential implications for gravity, cosmology, and condensed-matter analogues of QED in strong fields.

Abstract

We study the strong-field limit of a theory involving a quantum scalar field coupled to a vector background, which can be either an electromagnetic field or a non-gauge field coupled through the first derivative term. Our approach consists in obtaining resummed expressions for the associated heat kernels, from which we derive the corresponding resummed effective actions. These results allow us to discuss the effect of pair creation. Finally, we conjecture that resummations for more general theories should be possible.