Lie conformal algebra cohomology and the variational complex

We find an interpretation of the complex of variational calculus in terms of the Lie conformal algebra cohomology theory. This leads to a better understanding of both theories. In particular, we give an explicit construction of the Lie conformal algebra cohomology complex, and endow it with a structure of a g-complex. On the other hand, we give an explicit construction of the complex of variational calculus in terms of skew-symmetric poly-differential operators.Comment: 56 page

Geometric construction of modular functors from Conformal Field Theory

This is the second paper in a series of papers aimed at providing a geometric construction of modular functors and topological quantum field theories from conformal field theory building on the constructions in [TUY] and [KNTY]. We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [TUY] by a certain fractional power of the abelian theory first considered in [KNTY] and further studied in our first paper [AU1].Comment: Paper considerably expanded so as to make it self containe

Jacobi Identity for Vertex Algebras in Higher Dimensions

Vertex algebras in higher dimensions provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus techniques and investigating the notion of polylocal fields. We derive a Jacobi identity which together with the vacuum axiom can be taken as an equivalent definition of vertex algebra.Comment: 35 pages, references adde

Proton Zemach radius from measurements of the hyperfine splitting of hydrogen and muonic hydrogen

While measurements of the hyperfine structure of hydrogen-like atoms are traditionally regarded as test of bound-state QED, we assume that theoretical QED predictions are accurate and discuss the information about the electromagnetic structure of protons that could be extracted from the experimental values of the ground state hyperfine splitting in hydrogen and muonic hydrogen. Using recent theoretical results on the proton polarizability effects and the experimental hydrogen hyperfine splitting we obtain for the Zemach radius of the proton the value 1.040(16) fm. We compare it to the various theoretical estimates the uncertainty of which is shown to be larger that 0.016 fm. This point of view gives quite convincing arguments in support of projects to measure the hyperfine splitting of muonic hydrogen.Comment: Submitted to Phys. Rev.

Computation of cohomology of vertex algebras

We review cohomology theories corresponding to the chiral and classical operads. The first one is the cohomology theory of vertex algebras, while the second one is the classical cohomology of Poisson vertex algebras (PVA), and we construct a spectral sequence relating them. Since in “good” cases the classical PVA cohomology coincides with the variational PVA cohomology and there are well-developed methods to compute the latter, this enables us to compute the cohomology of vertex algebras in many interesting cases. Finally, we describe a unified approach to integrability through vanishing of the first cohomology, which is applicable to both classical and quantum systems of Hamiltonian PDEs

ON ТНЕ QUANTIТAТIVE DEТERMINATION OF CONCREMENTS

In our previous report the results were presented of comparative studies of methods for quantitative determination of calcium, magnesium, oxalate and phosphate ions in model solutions of concrements. The experimental data obtained indicate that the following methods may bе considered the most appropriate:1. Complexometric determination of Са2+ with 0,002 М solution of complexon III with fluorexon - thymolphthalein as indicator.2. Simultaneous complexometric determination of Са2-+ аnd Mg2 + а separate determination of Са2+ and detection of the amount of Mg2+ through the existing difference. 3. Plumbometric determination of C2O42 - with 0,1 М solution of Рb(NО3)2.4. Direct complexometric determination of РO43 - with 0,01 M solution of MgSO4. The purpose of the prelimiпary work was to evaluate contemporary methods for the determination of Ca2+, Mg2+, С2O42 - and РO43 - first оn model solutions аnd then on native concrements. In the present work some results are reported of the quantitative study of concrements of renal or vesical origin. The materials are obtained at the Surgical Clinic and the Propedeutic Iпternal Clinic at the Higher Medical Institute in Varna. Data presented are compaired with data obtained bу means of other methods

Precision Spectroscopy of Molecular Hydrogen Ions: Towards Frequency Metrology of Particle Masses

We describe the current status of high-precision ab initio calculations of the spectra of molecular hydrogen ions (H_2^+ and HD^+) and of two experiments for vibrational spectroscopy. The perspectives for a comparison between theory and experiment at a level of 1 ppb are considered.Comment: 26 pages, 13 figures, 1 table, to appear in "Precision Physics of Simple Atomic Systems", Lecture Notes in Physics, Springer, 200

ON ТНЕ QUANTIТAТIVE DEТERMINATION OF CONCREMENTS

The chemical composition of concrements has been of clinical interest for long. For that reason methods for its determination have already been devised. А method for the qualitative examination of concrements is proposed bу Halman. These methods are old in many respects and do not meet the present capacities of chemical analysis. А method for quantitative determination has been proposed also bу Schpet and Кeiser, but this method is neither contemporary.The interest shown in internal and urological practice toward the quantitative composition of concrements stimulated us to elaborate а method for quantitative analysis, primarily of renal and vesical concrements. We directed our attention mainly toward modern methods. Our definite experimental work consisted of the following: 1) comparative study of known methods on model solutions prepared bу us; 2) application of selected methods for definite analysis of concrements. We chose mainly complexometric methods which imvosed а necessity to specify the conditions for determination of Са +, Mg2+, C2O42-, РO43- in model solutions, resembling concrement solutions. The results are reported in the present work

Constructing quantum vertex algebras

This is a sequel to \cite{li-qva}. In this paper, we focus on the construction of quantum vertex algebras over \C, whose notion was formulated in \cite{li-qva} with Etingof and Kazhdan's notion of quantum vertex operator algebra (over \C[[h]]) as one of the main motivations. As one of the main steps in constructing quantum vertex algebras, we prove that every countable-dimensional nonlocal (namely noncommutative) vertex algebra over \C, which either is irreducible or has a basis of PBW type, is nondegenerate in the sense of Etingof and Kazhdan. Using this result, we establish the nondegeneracy of better known vertex operator algebras and some nonlocal vertex algebras. We then construct a family of quantum vertex algebras closely related to Zamolodchikov-Faddeev algebras.Comment: 37 page