Path-integral over non-linearly realized groups and Hierarchy solutions

The technical problem of deriving the full Green functions of the elementary pion fields of the nonlinear sigma model in terms of ancestor amplitudes involving only the flat connection and the nonlinear sigma model constraint is a very complex task. In this paper we solve this problem by integrating, order by order in the perturbative loop expansion, the local functional equation derived from the invariance of the SU(2) Haar measure under local left multiplication. This yields the perturbative definition of the path-integral over the non-linearly realized SU(2) group.Comment: 26 page

The Algebra of Physical Observables in Nonlinearly Realized Gauge Theories

We classify the physical observables in spontaneously broken nonlinearly realized gauge theories in the recently proposed loopwise expansion governed by the Weak Power-Counting (WPC) and the Local Functional Equation. The latter controls the non-trivial quantum deformation of the classical nonlinearly realized gauge symmetry, to all orders in the loop expansion. The Batalin-Vilkovisky (BV) formalism is used. We show that the dependence of the vertex functional on the Goldstone fields is obtained via a canonical transformation w.r.t. the BV bracket associated with the BRST symmetry of the model. We also compare the WPC with strict power-counting renormalizability in linearly realized gauge theories. In the case of the electroweak group we find that the tree-level Weinberg relation still holds if power-counting renormalizability is weakened to the WPC condition.Comment: 20 pages, 1 figur

Eu(iii) and Tb(iii) complexes of 6-fold coordinating ligands showing high affinity for the hydrogen carbonate ion: A spectroscopic and thermodynamic study

In the present contribution, four classes of Ln(iii) complexes (Ln = Eu and Tb) have been synthesized and characterized in aqueous solution. They differ by charge, Ln(bpcd)+ [bpcd2- = N,N'-bis(2-pyridylmethyl)-trans-1,2-diaminocyclohexane N,N'-diacetate] and Ln(bQcd)+ (bQcd2- = N,N'-bis(2-quinolinmethyl)-trans-1,2-diaminocyclohexane N,N'-diacetate) being positively charged and Ln(PyC3A) (PyC3A3- = N-picolyl-N,N',N'-trans-l,2-cyclohexylenediaminetriacetate) and Ln(QC3A) (QC3A3- = N-quinolyl-N,N',N'-trans-l,2-cyclohexylenediaminetriacetate) being neutral. Combined DFT, spectrophotometric and potentiometric studies reveal the presence, under physiological conditions (pH 7.4), of a couple of equally and highly stable isomers differing by the stereochemistry of the ligands (trans-N,N and trans-O,O for bpcd2- and bQcd2-; trans-O,O and trans-N,O for PyC3A3- and QC3A3-). Their high log\u2009\u3b2 values (9.97 < log\u2009\u3b2 < 15.68), the presence of an efficient antenna effect and the strong increase of the Ln(iii) luminescence intensity as a function of the hydrogen carbonate concentration in physiological solution, render these complexes as very promising optical probes for a selective detection of HCO3-in cellulo or in extracellular fluid. This particularly applies to the cationic Eu(bpcd)+, Tb(bpcd)+ and Eu(bQcd)+ complexes, which are capable of guesting up to two hydrogen carbonate anions in the inner coordination sphere of the metal ion, so that they show an unprecedented affinity towards HCO3- (log\u2009K for the formation of the adduct in the 4.6-5.9 range)

The anonymous subgraph problem

In this work we address the Anonymous Subgraph Problem (ASP). The problem asks to decide whether a directed graph contains anonymous subgraphs of a given family. This problem has a number of practical applications and here we describe three of them (Secret Santa Problem, anonymous routing, robust paths) that can be formulated as ASPs. Our main contributions are (i) a formalization of the anonymity property for a generic family of subgraphs, (ii) an algorithm to solve the ASP in time polynomial in the size of the graph under a set of conditions, and (iii) a thorough evaluation of our algorithms using various tests based both on randomly generated graphs and on real-world instances

A chiral lactate reporter based on total and circularly polarized Tb(iii) luminescence

The coordination features and signaling of a l-lactate ion by a [Tb(bpcd)]+(bpcd = N,N′-bis(2-pyridylmethyl)-trans-1,2-diaminocyclohexane-N,N′-diacetate) complex have been investigated by means of a combination of techniques, including total luminescence, calorimetry and circularly polarized luminescence. The l-lactate/[Tb(bpcd)]+association constant, determined by both luminescence titration and isothermal titration calorimetry, indicates a weak interaction (log K = 1.3-1.45) between the analyte and both enantiomers of the complex. The theoretical DFT calculations suggest that the most likely coordination of l-lactate to the possible stereoisomers of the [Tb(S,S-bpcd)]+complex (trans-O,O or trans-Npy,Npy) is one involving a hydroxyl group. The results of [Tb(rac-bpcd)]+as a chiroptical luminescent probe of l-lactate underline the peculiar role of the chiral 1,2-diaminocyclohexane (DACH) backbone. Indeed, the target anion is capable of inducing CPL activity in the racemic mixture of Tb complexes containing DACH-based ligands. The same is not observed for the achiral analogue [Tb(bped)]+(bped = N,N′-bis(2-pyridylmethyl)ethylenediamine-N,N′-diacetate) complex, likely because of the flexibility of the ethylenic group which allows an interconversion between different isomers which produces a null net CPL activity. Thanks to the differential quantum yield of the two diastereomeric species (R,R)-l and (S,S)-l, one can use the racemic complex to reveal l-lactate by measuring the induced CPL spectrum. Interestingly, this has been demonstrated in a commercial complex solution for medical use, containing several electrolytes, namely Ringer's lactate

Dynamics of the Energy Transfer Process in Eu(III) Complexes Containing Polydentate Ligands Based on Pyridine, Quinoline, and Isoquinoline as Chromophoric Antennae

In this work, we investigated from a theoretical point of view the dynamics of the energy transfer process from the ligand to Eu(III) ion for 12 isomeric species originating from six different complexes differing by nature of the ligand and the total charge. The cationic complexes present the general formula [Eu(L)(H2O)2]+ (where L = bpcd2- = N,N'-bis(2-pyridylmethyl)-trans-1,2-diaminocyclohexane N,N'-diacetate; bQcd2- = N,N'-bis(2-quinolinmethyl)-trans-1,2-diaminocyclohexane N,N'-diacetate; and bisoQcd2- = N,N'-bis(2-isoquinolinmethyl)-trans-1,2-diaminocyclohexane N,N'-diacetate), while the neutral complexes present the Eu(L)(H2O)2 formula (where L = PyC3A3- = N-picolyl-N,N',N'-trans-1,2-cyclohexylenediaminetriacetate; QC3A3- = N-quinolyl-N,N',N'-trans-1,2-cyclohexylenediaminetriacetate; and isoQC3A3- = N-isoquinolyl-N,N',N'-trans-1,2-cyclohexylenediaminetriacetate). Time-dependent density functional theory (TD-DFT) calculations provided the energy of the ligand excited donor states, distances between donor and acceptor orbitals involved in the energy transfer mechanism (RL), spin-orbit coupling matrix elements, and excited-state reorganization energies. The intramolecular energy transfer (IET) rates for both singlet-triplet intersystem crossing and ligand-to-metal (and vice versa) involving a multitude of ligand and Eu(III) levels and the theoretical overall quantum yields (ϕovl) were calculated (the latter for the first time without the introduction of experimental parameters). This was achieved using a blend of DFT, Judd-Ofelt theory, IET theory, and rate equation modeling. Thanks to this study, for each isomeric species, the most efficient IET process feeding the Eu(III) excited state, its related physical mechanism (exchange interaction), and the reasons for a better or worse overall energy transfer efficiency (ηsens) in the different complexes were determined. The spectroscopically measured ϕovl values are in good agreement with the ones obtained theoretically in this work