Abstract. As part of the work of the Economic Commission for Europe of the United Nations Task Force on Emission Inventories, a new set of guidelines has been developed for assessing the emissions of sulphur, nitrogen oxides, NH 3, CH4, and nonmethane volatile organic compounds (NMVOC) from biogenic and other natural sources in Europe. This paper gives the background to these guidelines, describes the sources, and gives our recommended methodologies for estimating emissions. We have assembled land use and other statistics from European or national compilations and present emission estimates for the various natural/biogenic source categories based on these.

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-Lemaître-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.

We extend the adiabatic regularization method by introducing an arbitrary mass scale µ in the construction of the subtraction terms. This allows us to obtain, in a very robust way, the running of the coupling constants by demanding µ-invariance of the effective semiclassical (Maxwell-Einstein) equations. In particular, we get the running of the electric charge of perturbative quantum electrodynamics. Furthermore, the method brings about a renormalization of the cosmological constant and the Newtonian gravitational constant. The running obtained for these dimensionful coupling constants has new relevant (non-logarithmic) contributions, not predicted by dimensional regularization.

We consider pair production phenomena in spatially homogeneous strong electric fields. We focus on spinor QED in two-dimensions and discuss the potential ambiguity in the adiabatic order assignment for the electromagnetic potential required to fix the renormalization subtractions. This ambiguity can be univocally fixed by imposing, at the semiclassical level, stress-energy conservation when both electric and gravitational backgrounds are present.

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.

We propose to slightly generalize the DeWitt-Schwinger adiabatic renormalization subtractions in curved space to include an arbitrary renormalization mass scale μ. The new predicted running for the gravitational couplings are fully consistent with decoupling of heavy massive fields. This is a somewhat improvement with respect to the more standard treatment of minimal (DeWitt-Schwinger) subtractions via dimensional regularization. We also show how the vacuum metamorphosis model emerges from the running couplings.

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. Furthermore, we also show a close relation between the breaking of the adiabatic invariance and the emergence of the axial anomaly.

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 stressenergy tensor T µν and the bilinear ψ ψ in a spatially flat Friedmann-Lemaitre-RobertsonWalker (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.