Using Covariant Polarisation Sums in QCD

Covariant gauges lead to spurious, non-physical polarisation states of gauge bosons. In QED, the use of the Feynman gauge, $$\sum _{\lambda } \varepsilon _\mu ^{(\lambda )}\varepsilon _\nu ^{(\lambda )*} = -\eta _{\mu \nu }$$ ∑ λ ε μ ( λ ) ε ν ( λ ) ∗ = - η μ ν , is justified by the Ward identity which ensures that the contributions of non-physical polarisation states cancel in physical observables. In contrast, the same replacement can be applied only to a single external gauge boson in squared amplitudes of non-abelian gauge theories like QCD. In general, the use of this replacement requires to include external Faddeev–Popov ghosts. We present a pedagogical derivation of these ghost contributions applying the optical theorem and the Cutkosky cutting rules. We find that the resulting cross terms $$\mathcal {A}(c_1,\bar{c}_1;\ldots )\mathcal {A}(\bar{c}_1,c_1;\ldots )^*$$ A ( c 1 , c ¯ 1 ; … ) A ( c ¯ 1 , c 1 ; … ) ∗ between ghost amplitudes cannot be transformed into $$(-1)^{n/2}|\mathcal {A}(c_1,\bar{c}_1;\ldots )|^2$$ ( - 1 ) n / 2 | A ( c 1 , c ¯ 1 ; … ) | 2 in the case of more than two ghosts. Thus the Feynman rule stated in the literature holds only for two external ghosts, while it is in general incorrect.

Analysis of fabrics and metal threads from two Andalusian liturgical vestments from the seventeenth and eighteenth centuries: a multitechnical approach

This manuscript provided one of the first scientific studies performed on ancient Spanish liturgical vestments by using a multitechnical physicochemical approach. The interlining and lining fabrics were done by cotton and the core of threads by silk. Silver, gold and little amounts of copper were detected. The highest values of gold were found in the metal threads of the cope and the gallon of the chasuble. Two layers were identified: the internal composed by silver and the external by silver and gold. The fibers were proved to be degraded and also the surface of the metal, where scratches and silver-based compounds were detected due to environmental and anthropogenic actions. Indigo was employed as dye in the blue and green fabrics. Wax was detected in the yellow fibers, although other dyes could not be discarded. The materials used in the restoration processes were of minor quality.

A critical assessment of extreme events trends in times of global warming

This article reviews recent bibliography on time series of some extreme weather events and related response indicators in order to understand whether an increase in intensity and/or frequency is detectable. The most robust global changes in climate extremes are found in yearly values of heatwaves (number of days, maximum duration and cumulated heat), while global trends in heatwave intensity are not significant. Daily precipitation intensity and extreme precipitation frequency are stationary in the main part of the weather stations. Trend analysis of the time series of tropical cyclones show a substantial temporal invariance and the same is true for tornadoes in the USA. At the same time, the impact of warming on surface wind speed remains unclear. The analysis is then extended to some global response indicators of extreme meteorological events, namely natural disasters, floods, droughts, ecosystem productivity and yields of the four main crops (maize, rice, soybean and wheat). None of these response indicators show a clear positive trend of extreme events. In conclusion on the basis of observational data, the climate crisis that, according to many sources, we are experiencing today, is not evident yet. It would be nevertheless extremely important to define mitigation and adaptation strategies that take into account current trends.