Adiabatic regularization for Dirac fields in timevarying electric backgrounds
Abstract
The adiabatic regularization method was originally proposed by Parker and Fulling to renormalize the energymomentum tensor of scalar fields in expanding universes. It can be extended to renormalize the electric current induced by quantized scalar fields in a timevarying 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 selfconsistent ansatz for the adiabatic expansion, in presence of a prescribed timedependent 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 SchwingerDeWitt adiabatic expansion of the twopoint function. We give the renormalized expression of the electric current and analyze, using numerical and analytical tools, the pair production induced by a Sautertype electric pulse. We also analyze the scaling properties of the current for a large field strength.
 Publication:

Physical Review D
 Pub Date:
 May 2020
 DOI:
 10.1103/PhysRevD.101.105014
 arXiv:
 arXiv:2001.08710
 Bibcode:
 2020PhRvD.101j5014B
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 17 pages, 2 figure, addition of one extra section