Beltran-Palau, P., Ferreiro, A., Navarro-Salas, J., & Pla, S. (2019). Breaking of adiabatic invariance in the creation of particles by electromagnetic backgrounds. Phys. Rev. D, 100(8), 085014–12pp.
Abstract: Particles are spontaneously created from the vacuum by time-varying gravitational or electromagnetic backgrounds. It has been proven that the particle number operator in an expanding universe is an adiabatic invariant. In this paper we show that, in some special cases, the expected adiabatic invariance of the particle number fails in presence of electromagnetic backgrounds. In order to do this, we consider as a prototype a Sauter-type electric pulse. Furthermore, we also show a close relation between the breaking of the adiabatic invariance and the emergence of the axial anomaly.
|
Navarro-Salas, J., & Pla, S. (2021). (F, G)-summed form of the QED effective action. Phys. Rev. D, 103(8), L081702–7pp.
Abstract: We conjecture that the proper-time series expansion of the one-loop effective Lagrangian of quantum electrodynamics can be summed in all terms containing the field-strength invariants F = 1/4F F-mu nu(mu nu) (x), G = 1/4 (F) over tilde F-mu nu(mu nu) (x), including those also possessing derivatives of the electromagnetic field strength. This partial resummation is exactly encapsulated in a factor with the same form as the Heisenberg-Euler Lagrangian density, except that now the electric and magnetic fields can depend arbitrarily on spacetime coordinates. We provide strong evidence for this conjecture, which is proved to sixth order in the proper time. Furthermore, and as a byproduct, we generate some solvable electromagnetic backgrounds. We also discuss the implications for a generalization of the Schwinger formula for pair production induced by nonconstant electric fields. Finally, we briefly outline the extension of these results in the presence of gravity.
|
Ferreiro, A., & Pla, S. (2022). Adiabatic regularization and preferred vacuum state for the lambda phi^4 field theory in cosmological spacetimes. Phys. Rev. D, 106(6), 065015–12pp.
Abstract: We extend the method of adiabatic regularization by introducing an arbitrary parameter μfor a scalar field with quartic self-coupling in a Friedmann-Lemaitre-Robertson-Walker spacetime at one-loop order. The subtraction terms constructed from this extended version allow us to define a preferred vacuum state at a fixed time ri 1/4 ri0 for this theory. We compute this vacuum state for two commonly used background fields in cosmology, specially in the context of preheating. We also give a possible prescription for an adequate value for mu.
|
Ferreiro, A., Navarro-Salas, J., & Pla, S. (2018). Role of gravity in the pair creation induced by electric fields. Phys. Rev. D, 98(4), 045015–6pp.
Abstract: We analyze the pair production induced by homogenous, time-dependent electric fields in an expanding space-time background. We point out that, in obtaining the semiclassical Maxwell equations, two distinct notions of adiabatic renormalization are possible. In Minkowski space, the two recipes turn out to be equivalent. However, in the presence of gravity, only the recipe requiring an adiabatic hierarchy between the gravitational and the gauge field is consistent with the conservation of the energy-momentum tensor.
|
Pla, S., & Winstanley, E. (2023). Equivalence of the adiabatic expansion and Hadamard renormalization for a charged scalar field. Phys. Rev. D, 107(2), 025004–22pp.
Abstract: We examine the relationship between three approaches (Hadamard, DeWitt-Schwinger, and adiabatic) to the renormalization of expectation values of field operators acting on a charged quantum scalar field. First, we demonstrate that the DeWitt-Schwinger representation of the Feynman Green's function is a particular case of the Hadamard representation. Next, we restrict attention to a spatially flat Friedmann-Lemaitre-Robertson-Walker universe with time-dependent, purely electric, background electromagnetic field, considering two-, three-, and four-dimensional space-times. Working to the order required for the renormalization of the stress-energy tensor, we find the adiabatic and DeWitt-Schwinger expansions of the Green's function when the space-time points are spatially separated. In two and four dimensions, the resulting DeWitt-Schwinger and adiabatic expansions are identical. In three dimensions, the DeWittSchwinger expansion contains terms of adiabatic order 4 that are not necessary for the renormalization of the stress-energy tensor and hence absent in the adiabatic expansion. The equivalence of the DeWittSchwinger and adiabatic approaches to renormalization in the scenario considered is thereby demonstrated in even dimensions. In odd dimensions the situation is less clear and further investigation is required in order to determine whether adiabatic renormalization is a locally covariant renormalization prescription.
|
