Nonlocal quantum field theory (QFT) of one-component scalar field ϕ in D-dimensional Euclidean spacetime is considered. The generating functional (GF) of complete Green functions Z as a functional of external source j, coupling constant g, and spatial measure dµ is studied. An expression for GF Z in terms of the abstract integral over the primary field ϕ is given. An expression for GF Z in terms of integrals over the primary field and separable Hilbert space (HS) is obtained by means of a separable expansion of the free theory inverse propagatorL over the separable HS basis. The classification of functional integration measures D [ϕ] is formulated, according to which trivial and two nontrivial versions of GF Z are obtained. Nontrivial versions of GF Z are expressed in terms of 1-norm and 0-norm, respectively. In the 1-norm case in terms of the original symbol for the product integral, the definition for the functional integration measure D [ϕ] over the primary field is suggested. In the 0-norm case, the definition and the meaning of 0-norm are given in terms of the replica-functional Taylor series. The definition of the 0-norm generator Ψ is suggested. Simple cases of sharp and smooth generators are considered. An alternative derivation of GF Z in terms of 0-norm is also given. All these definitions allow to calculate corresponding functional integrals over ϕ in quadratures. Expressions for GF Z in terms of integrals over the separable HS, aka the basis functions representation, with new integrands are obtained. For polynomial theories ϕ 2n , n = 2, 3, 4, . . . , and for the nonpolynomial theory sinh 4 ϕ, integrals over the separable HS in terms of a power series over the inverse coupling constant 1/ √ g for both norms (1-norm and 0-norm) are calculated. Thus, the strong coupling expansion in all theories considered is given. "Phase transitions" and critical values of model parameters are found numerically. A generalization of the theory to the case of the uncountable integral over HS is formulated: GF Z for an arbitrary QFT and the strong coupling expansion for the theory ϕ 4 are derived. Finally a comparison of two GFs Z, one on the continuous lattice of functions and one obtained using the Parseval-Plancherel identity, is given.
Organophosphate-chloride complexes [{(2,6-iPr2C6H3-O)2POO}2LnCl(CH3OH)4]·2CH3OH, Ln = Nd (1), Eu (2), Gd (3), and Tb (4) have been obtained and structurally characterized. Their reaction with 2,2′:6′,2″-terpyridine leads to the formation of 1:1 adducts ([{(2,6-iPr2C6H3-O)2POO}2LnCl(terpy)(H2O)2(CH3OH)], Ln = Eu (5), Gd (6), Tb (7) with exception of Nd, where tris-diisopropylphenylphosphate complex [{(2,6-iPr2C6H3-O)2POO}3Nd) (terpy)(H2O)(CH3OH)] (8) was obtained due to the ligand metathesis. A bright luminescence observed for the Eu and Tb organophosphate complexes is the first example of an application of organophosphate ligands for 4f-ions luminescence sensitization. Photophysical properties of all complexes were analyzed by optical spectroscopy and an energy transfer scheme was discussed. A combination of two types of ligands into the coordination sphere (phosphate and phenanthroline) allows designing the Eu surrounding with very high intrinsic quantum yield QEuEu (0.92) and highly luminescent Ln complexes for both visible and near-infrared (NIR) regions.
The crystal structure of the complex {Eu[O2P(O-2,6-iPr2C6H3)2]3(CH3OH)5}·CH3OH, which exhibits intra- and intermolecular O—H⋯O hydrogen bonding, and its luminescent properties have been studied.
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