Beltran-Palau, P., Navarro-Salas, J., & Pla, S. (2020). Adiabatic regularization for Dirac fields in time-varying electric backgrounds. Phys. Rev. D, 101(10), 105014–15pp.
Abstract: The adiabatic regularization method was originally proposed by Parker and Fulling to renormalize the energy-momentum tensor of scalar fields in expanding universes. It can be extended to renormalize the electric current induced by quantized scalar fields in a time-varying electric background. This can be done in a way consistent with gravity if the vector potential is considered as a variable of adiabatic order one. Assuming this, we further extend the method to deal with Dirac fields in four space-time dimensions. This requires a self-consistent ansatz for the adiabatic expansion, in presence of a prescribed time-dependent electric field, which is different from the conventional expansion used for scalar fields. Our proposal is consistent, in the massless limit, with the conformal anomaly. We also provide evidence that our proposed adiabatic expansion for the fermionic modes parallels the Schwinger-DeWitt adiabatic expansion of the two-point function. We give the renormalized expression of the electric current and analyze, using numerical and analytical tools, the pair production induced by a Sauter-type electric pulse. We also analyze the scaling properties of the current for a large field strength.
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Beltran-Palau, P., del Rio, A., & Navarro-Salas, J. (2023). Quantum corrections to the Schwarzschild metric from vacuum polarization. Phys. Rev. D, 107(8), 085023–15pp.
Abstract: We explore static and spherically symmetric solutions of the 4-dimensional semiclassical Einstein's equations using the quantum vacuum polarization of a conformal field as a source. These solutions may be of interest for the study of exotic compact objects (ECOs). The full backreaction problem is addressed by solving the semiclassical Tolman-Oppenheimer-Volkoff (TOV) equations making use of effective equations of state inspired by the trace anomaly and an extra simplifying and reasonable assumption. We combine analytical and numerical techniques to solve the resulting differential equations, both perturbatively and nonperturbatively in h. In all cases the solution is similar to the Schwarzschild metric up p ffiffito the vicinity of the classical horizon r = 2M. However, at r = 2M + epsilon, with epsilon similar to O(root h), we find a coordinate singularity. In the case of matching with a static star, this leads to an upper bound in the compactness, and sets a constraint on the family of stable ECOs. We also study the corrections that the quantum-vacuum polarization induces on the propagation of waves, and discuss the implications. For the pure vacuum case, we can further extend the solution by using appropriate coordinates until we reach another singular point, where this time a null curvature singularity arises and prevents extending beyond. This picture qualitatively agrees with the results obtained in the effective two-dimensional approach, and reinforces the latter as a reasonable method.
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Bernabeu, J., & Navarro-Salas, J. (2019). A Non-Local Action for Electrodynamics: Duality Symmetry and the Aharonov-Bohm Effect, Revisited. Symmetry-Basel, 11(10), 1191–13pp.
Abstract: A non-local action functional for electrodynamics depending on the electric and magnetic fields, instead of potentials, has been proposed in the literature. In this work we elaborate and improve this proposal. We also use this formalism to confront the electric-magnetic duality symmetry of the electromagnetic field and the Aharonov-Bohm effect, two subtle aspects of electrodynamics that we examine in a novel way. We show how the former can be derived from the simple harmonic oscillator character of vacuum electrodynamics, while also demonstrating how the magnetic version of the latter naturally arises in an explicitly non-local manner.
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del Rio, A., Ferreiro, A., Navarro-Salas, J., & Torrenti, F. (2017). Adiabatic regularization with a Yukawa interaction. Phys. Rev. D, 95(10), 105003–19pp.
Abstract: We extend the adiabatic regularization method for an expanding universe to include the Yukawa interaction between quantized Dirac fermions and a homogeneous background scalar field. We give explicit expressions for the renormalized expectation values of the stress-energy tensor < T-mu nu > and the bilinear <(psi) over bar psi > in a spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. These are basic ingredients in the semiclassical field equations of fermionic matter in curved spacetime interacting with a background scalar field. The ultraviolet subtracting terms of the adiabatic regularization can be naturally interpreted as coming from appropriate counterterms of the background fields. We fix the required covariant counterterms. To test our approach we determine the contribution of the Yukawa interaction to the conformal anomaly in the massless limit and show its consistency with the heat-kernel method using the effective action.
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del Rio, A., Navarro-Salas, J., & Torrenti, F. (2014). Renormalized stress-energy tensor for spin-1/2 fields in expanding universes. Phys. Rev. D, 90(8), 084017–15pp.
Abstract: We provide an explicit expression for the renormalized expectation value of the stress-energy tensor of a spin-1/2 field in a spatially flat Friedmann-Lemaitre-Robertson-Walker universe. Its computation is based on the extension of the adiabatic regularization method to fermion fields introduced recently in the literature. The tensor is given in terms of UV-finite integrals in momentum space, which involve the mode functions that define the quantum state. As illustrative examples of the method efficiency, we see how to compute the renormalized energy density and pressure in two interesting cosmological scenarios: a de Sitter spacetime and a radiation-dominated universe. In the second case, we explicitly show that the late-time renormalized stress-energy tensor behaves as that of classical cold matter. We also check that, if we obtain the adiabatic expansion of the scalar field mode functions with a similar procedure to the one used for fermions, we recover the well-known WKB-type expansion.
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