In strong (quasi–)Abelian fields, quantum fluctuations of fermions induce an effective Lagrangian density whose imaginary (absorptive) part is purely nonperturbative and known to be responsible for the fermion–antifermion pair creation. On the other hand, the induced real (dispersive) part has perturbative and nonperturbative contributions. We argue how to separate the two contributions from ea...

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Theorem 1.1 (Chudnovsky’s theorems). Let Λ = Zω+Zω′ ⊂ C be a lattice with invariants g2, g3, Weierstrass functions ℘, ζ and quasi-periods η, η′, all defined in the usual way (see [Sil94]). Each of the sets below contains at least two algebraically independent numbers : first (1) {g2, g3, η ω , π ω}, (2) {g2, g3, ω, η, ω′, η′}; if we assume g2, g3 ∈ Q̄ : (3) { η ω , π ω}, (4) {ω, ω′, η, η′}; and ...

It is natural to extend the Grothendieck theorem on completeness, valid for locally convex topological vector spaces, to Abelian topological groups. The adequate framework to do it seems to be the class of locally quasi-convex groups. However, in this paper we present examples of metrizable locally quasi-convex groups for which the analogue to the Grothendieck theorem does not hold. By means of...

For an abelian topological group G, let Ĝ denote the dual group of all continuous characters endowed with the compact open topology. Given a closed subset X of an infinite compact abelian group G such that w(X) < w(G), and an open neighbourhood U of 0 in T, we show that |{χ ∈ Ĝ : χ(X) ⊆ U}| = |Ĝ|. (Here, w(G) denotes the weight of G.) A subgroup D of G determines G if the map r : Ĝ → D̂ defined ...