The gauge-fixing parameter ξ dependence of two-point gauge variant correlation functions is studied for QED and QCD. We show that, in three Euclidean dimensions, or for four-dimensional thermal gauge theories, the usual procedure of getting a general covariant gauge-fixing term by averaging over a class of covariant gauge-fixing conditions leads to a nontrivial gauge-fixing parameter dependence...

An ordering of multidimensional alternatives is separable on a set of dimensions if fixing values on the complementary dimensions always produces the same induced ordering. Most often, studies of separability assume continuous alternative spaces; as we show, separability has different properties when alternative spaces are discrete. For instance, two well-known theorems of Gorman—that common se...

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BACKGROUND Symbiotic nitrogen (N)-fixing trees are rare in late-successional temperate forests, even though these forests are often N limited. Two hypotheses could explain this paradox. The 'phylogenetic constraints hypothesis' states that no late-successional tree taxa in temperate forests belong to clades that are predisposed to N fixation. Conversely, the 'selective constraints hypothesis' s...