Beltran-Palau, P., Navarro-Salas, J., & Pla, S. (2019). Translational anomaly of chiral fermions in two dimensions. Phys. Rev. D, 99(10), 105008–5pp.
Abstract: It is well known that a quantized two-dimensional Weyl fermion coupled to gravity spoils general covariance and breaks the covariant conservation of the energy-momentum tensor. In this brief article, we point out that the quantum conservation of the momentum can also fail in flat spacetime, provided the Weyl fermion is coupled to a time-varying homogeneous electric field. This signals a quantum anomaly of the space-translation symmetry, which has not been highlighted in the literature so far.
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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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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. (2014). Spacetime correlators of perturbations in slow-roll de Sitter inflation. Phys. Rev. D, 89(8), 084037–7pp.
Abstract: Two-point correlators and self-correlators of primordial perturbations in quasi-de Sitter spacetime backgrounds are considered. For large separations two-point correlators exhibit nearly scale invariance, while for short distances self-correlators need standard renormalization. We study the deformation of two-point correlators to smoothly match the self-correlators at coincidence. The corresponding angular power spectrum is evaluated in the Sachs-Wolfe regime of low multipoles. Scale invariance is maintained, but the amplitude of C(l)could change in a nontrivial way.
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