Sebastián A. Franchino-Viñas

A bstract: Building upon the Covariant Derivative Expansion, we develop a method to compute effective actions that is able to capture non-perturbative effects induced by strong background fields. We demonstrate the method in scalar QED, by deriving the full second-derivative corrections to the scalar Heisenberg-Euler effective action. The corresponding result is interpreted as an effective field theory with three characteristic scales, two of which are large (mass and field strength) in comparison with the remaining one (derivatives of the field). As an application, we show that, at this order, the transseries structure of the Schwinger pair production rate is preserved, even if the involved coefficients are modified. Our analysis also helps clarify recent disagreements concerning the coefficients of this effective action.

Among the available perturbative approaches in quantum field theory, heat kernel techniques provide a powerful and geometrically transparent framework for computing effective actions in nontrivial backgrounds. In this work, resummation patterns within the heat kernel expansion are examined as a means of systematically extracting nonperturbative information. Building upon previous results for Yukawa interactions and scalar quantum electrodynamics, we extend the analysis to spinor fields, demonstrating that a recently conjectured resummation structure continues to hold. The resulting formulation yields a compact expression that resums invariants constructed from the electromagnetic tensor and its spinorial couplings, while preserving agreement with known proper-time coefficients. Beyond its immediate computational utility, the framework offers a unified perspective on the emergence of nonperturbative effects (such as Schwinger pair creation) in relation to perturbative heat kernel data, and provides a basis for future extensions to curved spacetimes and non-Abelian gauge theories.

We advocate that the dual picture of spacetime noncommutativity , i.e. the existence of a curved momentum space, could be a way out to solve some of the open conceptual problems in the field, such as the basis dependence of observables. In this framework, we show how to build deformed Klein--Gordon and Dirac equations. In addition, we give an outlook of how one could define quantum field theories, both free and interacting ones.

Building upon the Covariant Derivative Expansion, we develop a method to compute effective actions that is able to capture non-perturbative effects induced by strong background fields. We demonstrate the method in scalar QED, by deriving the full second-derivative corrections to the scalar Heisenberg--Euler effective action. The corresponding result is interpreted as an effective field theory with three characteristic scales, two of which are large (mass and field strength) in comparison with the remaining one (derivatives of the field). As an application, we show that, at this order, the transseries structure of the Schwinger pair production rate is preserved, even if the involved coefficients are modified. Our analysis also helps clarify recent disagreements concerning the coefficients of this effective action.

A bstract: We adapt the Worldline Formalism to obtain resummed expressions for the effective action and the heat kernel of a quantum scalar field coupled to a Yukawa background. The resummation includes all the invariants built from powers, first derivatives and second derivatives of the latter. Using such results, we compute the instability of the vacuum computing the vacuum persistence amplitude and the corresponding Schwinger pair production probability. We show that the inclusion of an additional, rapidly varying background can greatly enhance the production of pairs.

We compute the particle creation rate in the context of quantum fields in curved spacetimes by evaluating the imaginary part of the effective action up to second order in the curvatures. For arbitrary metrics in dimensions D ≥ 4 , we express the vacuum persistence amplitude in terms of the Ricci scalar and the Weyl tensor, showing that, up to their second power, no particle creation occurs for conformal fields in conformally flat spacetimes. We pinpoint an analogy with the electromagnetic pair creation by writing the squared Weyl tensor invariant in terms of its electric and magnetic parts. In addition, we present an alternative expression for the imaginary part of the effective action employing the Cotton tensor. This is particularly useful in D = 3 , where the Weyl tensor trivially vanishes and the Cotton tensor is related to conformal flatness. Finally, we highlight the importance of the threshold for particle creation, a point that has been overlooked in some recent studies.

Quantum field theory predicts a nonlinear response of the vacuum to strong electromagnetic fields of macroscopic extent. This fundamental tenet has remained experimentally challenging and is yet to be tested in the laboratory. A particularly distinct signature of the resulting optical activity of the quantum vacuum is vacuum birefringence. This offers an excellent opportunity for a precision test of nonlinear quantum electrodynamics in an uncharted parameter regime. Recently, the operation of the high-intensity Relativistic Laser at the X-ray Free Electron Laser provided by the Helmholtz International Beamline for Extreme Fields has been inaugurated at the High Energy Density scientific instrument of the European X-ray Free Electron Laser. We make the case that this worldwide unique combination of an X-ray free-electron laser and an ultra-intense near-infrared laser together with recent advances in high-precision X-ray polarimetry, refinements of prospective discovery scenarios and progress in their accurate theoretical modelling have set the stage for performing an actual discovery experiment of quantum vacuum nonlinearity.

We review recent discussions concerning the definition of a quantum field theory in a curved and noncommutative space, the Snyder--de Sitter space. For a quartic self-interacting scalar field in a spacetime of arbitrary dimension, we show how to perturbatively define the classical action in the small-deformation regime and give its explicit first-order expression. Afterwards, we compute the divergences of the one-loop effective action for the two- and four-dimensional cases. These are employed to calculate the beta functions of the couplings and to numerically analyze the corresponding renormalization group flow. Depending on the initial conditions of the couplings, in four dimensions it is possible to obtain an asymptotic-free theory or a flip in the sign of the cosmological constant as a consequence of the running.

The article by van de Ven (1998 Class. Quantum Grav. 15 2311–44), is one of the fundamental references for higher-order heat kernel coefficients in curved backgrounds and with non-Abelian gauge connections. In this manuscript, we point out two errors and ambiguities in the a 5 coefficient, which may also affect the higher-order ones.