Towards a quantum field theory of primitive string fields

We denote generating functions of massless even higher spin fields "primitive string fields" (PSF's). In an introduction we present the necessary definitions and derive propagators and currents of these PDF's on flat space. Their off-shell cubic interaction can be derived after all off-shell cubic interactions of triplets of higher spin fields have become known [2],[3]. Then we discuss four-point functions of any quartet of PSF's. In subsequent sections we exploit the fact that higher spin field theories in $AdS_{d+1}$ are determined by AdS/CFT correspondence from universality classes of critical systems in $d$ dimensional flat spaces. The O(N) invariant sectors of the O(N) vector models for $1\leq N \leq \infty$ play for us the role of "standard models", for varying $N$, they contain e.g. the Ising model for N=1 and the spherical model for $N=\infty$. A formula for the masses squared that break gauge symmetry for these O(N) classes is presented for d = 3. For the PSF on $AdS$ space it is shown that it can be derived by lifting the PSF on flat space by a simple kernel which contains the sum over all spins. Finally we use an algorithm to derive all symmetric tensor higher spin fields. They arise from monomials of scalar fields by derivation and selection of conformal (quasiprimary) fields. Typically one monomial produces a multiplet of spin $s$ conformal higher spin fields for all $s \geq 4$, they are distinguished by their anomalous dimensions (in $CFT_3$) or by their mass (in $AdS_4$). We sum over these multiplets and the spins to obtain "string type fields", one for each such monomial.Comment: 16 pages,Late

ST-HM equipment consolidation

In general all kind of equipment must be maintained if it is to fulfil its function for a useful life. This can be achieved using one of the four key maintenance strategies - on failure maintenance, fixed time maintenance, condition based maintenance and design out maintenance. Each of these strategies has a place within an optimised maintenance plan. The first three maintenance strategies are mostly applied and implemented in the various ST maintenance plans. The fourth strategy in contrast, design out maintenance (also referred to as equipment consolidation / replacement), is rather applied in an ad-hoc strategy than in an organised way. This paper shall outline the general factors that must be considered in order to implement design out maintenance. Furthermore this paper shall demonstrate a possible approach for the application of design out maintenance regarding transport and handling equipment

Exact solvability of the Calogero and Sutherland models

Translationally invariant symmetric polynomials as coordinates for n-body problems with identical particles are proposed. It is shown that in those coordinates the Calogero and Sutherland n-body Hamiltonians after appropriate gauge transformations can be presented as a {\it quadratic} polynomial in the generators of the algebra sl_n in finite-dimensional degenerate representations. The exact solvability of these models follows from the existence of the infinite flags of such representation spaces preserved by above Hamiltonians

Exactly solvable potentials of Calogero type for q-deformed Coxeter groups

We establish that by parameterizing the configuration space of a one-dimensional quantum system by polynomial invariants of q-deformed Coxeter groups it is possible to construct exactly solvable models of Calogero type. We adopt the previously introduced notion of solvability which consists of relating the Hamiltonian to finite dimensional representation spaces of a Lie algebra. We present explicitly the $G_2^q$-case for which we construct the potentials by means of suitable gauge transformations.Comment: 22 pages Late

Multiple algebraisations of an elliptic Calogero-Sutherland model

Recently, Gomez-Ullate et al. (1) have studied a particular N-particle quantum problem with an elliptic function potential supplemented by an external field. They have shown that the Hamiltonian operator preserves a finite dimensional space of functions and as such is quasi exactly solvable (QES). In this paper we show that other types of invariant function spaces exist, which are in close relation to the algebraic properties of the elliptic functions. Accordingly, series of new algebraic eigenfunctions can be constructed.Comment: 9 Revtex pages, 3 PS-figures; Summary, abstract and conclusions extende

Structural motifs of pre-nucleation clusters

Structural motifs of pre-nucleation clusters prepared in single, optically levitated supersaturated aqueous aerosol microparticles containing CaBr2 as a model system are reported. Cluster formation is identified by means of X-ray absorption in the Br K-edge regime. The salt concentration beyond the saturation point is varied by controlling the humidity in the ambient atmosphere surrounding the 15–30 μm microdroplets. This leads to the formation of metastable supersaturated liquid particles. Distinct spectral shifts in near-edge spectra as a function of salt concentration are observed, in which the energy position of the Br K-edge is red-shifted by up to 7.1 ± 0.4 eV if the dilute solution is compared to the solid. The K-edge positions of supersaturated solutions are found between these limits. The changes in electronic structure are rationalized in terms of the formation of pre- nucleation clusters. This assumption is verified by spectral simulations using first-principle density functional theory and molecular dynamics calculations, in which structural motifs are considered, explaining the experimental results. These consist of solvated CaBr2 moieties, rather than building blocks forming calcium bromide hexahydrates, the crystal system that is formed by drying aqueous CaBr2 solutions

Basis States for Relativistic, Dynamically-Entangled Particles

In several recent papers on entanglement in relativistic quantum systems and relativistic Bell's inequalities, relativistic Bell-type two-particle states have been constructed in analogy to non-relativistic states. These constructions do not have the form suggested by relativistic invariance of the dynamics. Two relativistic formulations of Bell-type states are shown for massive particles, one using the standard Wigner spin basis and one using the helicity basis. The construction hinges on the use of Clebsch-Gordan coefficients of the Poincar\'e group to reduce the direct product of two unitary irreducible representations (UIRs) into a direct sum of UIRs.Comment: 19 pages, three tables, revte

Local Interactions of Higher-Spin Potentials That are Gauge Invariant in Linear Approximation

We study connected Wightman functions of $N$ conserved currents, each of which is formed from a scalar field and has even spin $l_{i}$. The UV divergence of this vertex function is regularized by the analytic continuation in the space dimension $D\longrightarrow D-\epsilon$. We evaluate the residue of $\epsilon ^{-1}$ only, which is a local interaction Lagrangian density and gauge invariant in linearComment: Talk given at Group XXVII Yerevan, Armenia, August 13-29, 2008, v.2 published in Yadernaya Fizika 73 (2010) 518-52

Gravitation on a Homogeneous Domain

Among all plastic deformations of the gravitational Lorentz vacuum \cite{wr1} a particular role is being played by conformal deformations. These are conveniently described by using the homogeneous space for the conformal group SU(2,2)/S(U(2)x U(2)) and its Shilov boundary - the compactified Minkowski space \tilde{M} [1]. In this paper we review the geometrical structure involved in such a description. In particular we demonstrate that coherent states on the homogeneous Kae}hler domain give rise to Einstein-like plastic conformal deformations when extended to \tilde{M} [2].Comment: 10 pages, 1 figure; four misprints in the original version corrected: one lacking closing parenthesis, two letters, and an overall sign in front of the primitive function on p.

The minimal conformal O(N) vector sigma model at d=3

For the minimal O(N) sigma model, which is defined to be generated by the O(N) scalar auxiliary field alone, all n-point functions, till order 1/N included, can be expressed by elementary functions without logarithms. Consequently, the conformal composite fields of m auxiliary fields possess at the same order such dimensions, which are m times the dimension of the auxiliary field plus the order of differentiation.Comment: 15 page