On the covariant structure of the two-point function

The spectral representation of the two-point function for arbitrary fields proposed recently [1] is rigorously proved and analyzed. The problem is treated in momentum space where the covariant structure is simpler because of the spectrum conditions. For finite-component fields the explicit matrix structure is found in coordinate space too and is applied to the definition of time-ordered Green functions for arbitrary spin. The decomposition of the two-point function into kernels of definite spin is carried out in the general case, a necessary and sufficient condition for the growth of the coefficients in this decomposition being given. The positive-definiteness condition (in the case of Hermitian conjugate fields) is fulfilled automatically by the elementary kernels.The formalism of homogeneous distributions in two dimensional complex domain [2] is used throughout the paper.On leave of absence from Joint Institute for Nuclear Research, Dubna, USSR and from Physical Institute of the Bulgarian Academy of Sciences, Sofia, Bulgaria.     

A simple automatic system using the HP-85 microcomputer for programmed potentiometric titration

A simple way of constructing an automatic titration system is proposed, based on combination of a digital pH-meter and an automatic burette with an HP-85 microcomputer. An inexpensive interface unit based on a MOTOROLA 6800 has been developed, which permits communication of the computer with the pH-meter and the burette. The system constructed is very flexible and can find wide application in potentiometric titration and direct potentiometry with different kinds of ion-selective electrodes.     

Scale and conformal covariance in quantum electrodynamics

The paper consists of two independent parts. First, we review the situationin scale invariant massless QED from an axiomatic standpoint. Assuming that the τ-functions (or, equivalently, the Euclidean Schwinger functions) transform covariantly under dilatations, we deduce that the current j_τ(x) has zero n-point Wightman functions, but nonvanishing τ-functions. Assuming in addition conformal invariance of the current-field vertex function, we write down a bootstrap equation similar to the one derived in [7] from the point of view of pertubation theory. Next we consider a non-Lagrangian, conformal invariant model of interacting antisymmetric tensor field F_μv (of scale dimension d) and Dirac field ψ (of dimension d'. The model involves two conserved currents (an “electric” and a “magnetic” one) and two effective coupling constants. We demonstrate that it is free of ultravioletdivergences in the range of dimensions $\text{2 < d < 3,}\text{3}\text{2}\text{< d′ <}\text{5}\text{2}$.     

Limite de convexité d'une classe de Nevanlinna de fonctions analytiques

Sans résumé     

On the possible multi-valuedness of quantum wavefunctions

A theorem generalizing a result due to Schrödinger on the possible multi-valuedness of quantum wavefunctions is proved. Relevant examples show that double-valued wavefunctions do exist, at least in problems of a theoretical interest.     

Reducing-difference infrared spectral analysis of cis- and trans-configurated lactams

The conventional (non-polarized) and linear-polarized IR-spectra of 2-pyrrolidone and laurolactam as typical representatives of lactams with cis- and trans-amide configuration, respectively, were studied by means of difference IR-spectroscopy. The application of this method to treatment of the non-polarized IR-spectra permits additional conclusions about the likely self-associates of these compounds dissolved in aprotic solvents. By means of the difference linear-dichroic IR-spectroscopy, a more precise assignment of the characteristic bands of the lactam cis- and trans-peptide forms as well as their stereo structures were accomplished. A comparative analysis with the linear-dichroic IR-spectra of epsilon-caprolactam and caprylolactam, as similar compounds, with cis- and trans-conformation, respectively, was also carried out.     

Motzkin decomposition of closed convex sets

Theodore Motzkin proved, in 1936, that any polyhedral convex set can be expressed as the (Minkowski) sum of a polytope and a polyhedral convex cone. This paper provides five characterizations of the larger class of closed convex sets in finite dimensional Euclidean spaces which are the sum of a compact convex set with a closed convex cone. These characterizations involve different types of representations of closed convex sets as the support functions, dual cones and linear systems whose relationships are also analyzed in the paper. The obtaining of information about a given closed convex set F and the parametric linear optimization problem with feasible set F from each of its different representations, including the Motzkin decomposition, is also discussed.