Landete, A., Navarro-Salas, J., & Torrenti, F. (2013). Adiabatic regularization for spin-1/2 fields. Phys. Rev. D, 88(6), 061501–5pp.
Abstract: We extend the adiabatic regularization method to spin-1/2 fields. The ansatz for the adiabatic expansion for fermionic modes differs significantly from the WKB-type template that works for scalar modes. We give explicit expressions for the first adiabatic orders and analyze particle creation in de Sitter spacetime. As for scalar fields, the adiabatic method can be distinguished by its capability to overcome the UV divergences of the particle number operator. We also test the consistency of the extended method by working out the conformal and axial anomalies for a Dirac field in a Friedmann-Lemaitre-Robertson-Walker spacetime, in exact agreement with those obtained from other renormalization prescriptions. We finally show its power by computing the renormalized stress-energy tensor for Dirac fermions in de Sitter space.
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Marañon-Gonzalez, F. J., & Navarro-Salas, J. (2023). Adiabatic regularization for spin-1 fields. Phys. Rev. D, 108(12), 125001–11pp.
Abstract: We analyze the adiabatic regularization scheme to renormalize Proca fields in a four-dimensional Friedmann-Lemaitre-Robertson-Walker spacetime. The adiabatic method is well established for scalar and spin-1/2 fields, but is not yet fully understood for spin-1 fields. We give the details of the construction and show that, in the massless limit, the renormalized stress-energy tensor of the Proca field is closely related to that of a minimally coupled scalar field. Our result is in full agreement with other approaches, based on the effective action, which also show a discontinuity in the massless limit. The scalar field can be naturally regarded as a Stueckelberg-type field. We also test the consistency of our results in de Sitter space.
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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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Landete, A., Navarro-Salas, J., & Torrenti, F. (2014). Adiabatic regularization and particle creation for spin one-half fields. Phys. Rev. D, 89(4), 044030–13pp.
Abstract: The extension of the adiabatic regularization method to spin-1/2 fields requires a self-consistent adiabatic expansion of the field modes. We provide here the details of such expansion, which differs from the WKB ansatz that works well for scalars, to firmly establish the generalization of the adiabatic renormalization scheme to spin-1/2 fields. We focus on the computation of particle production in de Sitter spacetime and obtain an analytic expression of the renormalized stress-energy tensor for Dirac fermions.
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Barbero, J. F., Ferreiro, A., Navarro-Salas, J., & Villaseñor, E. J. S. (2018). Adiabatic expansions for Dirac fields, renormalization, and anomalies. Phys. Rev. D, 98(2), 025016–11pp.
Abstract: We introduce an iterative method to univocally determine the adiabatic expansion of the modes of Dirac fields in spatially homogeneous external backgrounds. We overcome the ambiguities found in previous studies and use this new procedure to improve the adiabatic regularization/renormalization scheme. We provide details on the application of the method for Dirac fields living in a four-dimensional Friedmann-Lemaitre-Robertson-Walker spacetime with a Yukawa coupling to an external scalar field. We check the consistency of our proposal by working out the conformal anomaly. We also analyze a two-dimensional Dirac field in Minkowski space coupled to a homogeneous electric field and reproduce the known results on the axial anomaly. The adiabatic expansion of the modes given here can be used to properly characterize the allowed physical states of the Dirac fields in the above external backgrounds.
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