Adiabatic regularization for Dirac fields in time-varying electric backgrounds

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 spacetime 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.

Running gravitational couplings, decoupling, and curved spacetime renormalization

“…We also have exact agreement for the dimensionless coupling constants obtained from MS, as displayed in (9). Hadamard renormalization also leads to a similar result for the running of the electric coupling constant [24,29].…”

Physical scale adiabatic regularization in cosmological spacetimes

“…Adiabatic expansions for these scenarios have been developed for scalars [79] and fermions [80], which could be a nice starting point to build a PSAR method for these setups. Our method could also be potentially extended to the case of quantum fields with interactions to classical electric fields [81][82][83].…”

The physics of adiabatic particle number in the Schwinger effect

“…This supports our interpretation of the adiabatic particle number as an observable. It would, in this light, be very interesting to reconsider the properties of operators other than the number of pairs, such as the current, its adiabatic approximations, and their renormalisation [28,57,58].…”