Integrability of the Wess_Zumino-Witten model as a non-ultralocal theory

We consider the 2--dimensional Wess--Zumino--Witten (WZW) model in the canonical formalism introduced in a previous paper by two of us. Using an $r$--$s$ matrix approach to non--ultralocal field theories we find the Poisson algebra of monodromy matrices and of conserved quantities with a new, non--dynamical, $r$ matrix.Comment: Revised version. 3 references added. 13 pages, latex, no figure

Hidden Quantum Group Symmetry in the Chiral Model

We apply the SL(2,C) lattice Kac-Moody algebra of Alekseev, Faddeev and Semenov-Tian-Shansky to obtain a new lattice description of the SU(2) chiral model in two dimensions. The system has a global quantum group symmetry and it can be regarded as a deformation of two different theories. One is the nonabelian Toda lattice which is obtained in the limit of infinite central charge, while the other is a nonstandard Hamiltonian description of the chiral model obtained in the continuum limit.Comment: Latex file, 23 page

Spectral extension of the quantum group cotangent bundle

The structure of a cotangent bundle is investigated for quantum linear groups GLq(n) and SLq(n). Using a q-version of the Cayley-Hamilton theorem we construct an extension of the algebra of differential operators on SLq(n) (otherwise called the Heisenberg double) by spectral values of the matrix of right invariant vector fields. We consider two applications for the spectral extension. First, we describe the extended Heisenberg double in terms of a new set of generators -- the Weyl partners of the spectral variables. Calculating defining relations in terms of these generators allows us to derive SLq(n) type dynamical R-matrices in a surprisingly simple way. Second, we calculate an evolution operator for the model of q-deformed isotropic top introduced by A.Alekseev and L.Faddeev. The evolution operator is not uniquely defined and we present two possible expressions for it. The first one is a Riemann theta function in the spectral variables. The second one is an almost free motion evolution operator in terms of logarithms of the spectral variables. Relation between the two operators is given by a modular functional equation for Riemann theta function.Comment: 38 pages, no figure

Exact conserved quantities on the cylinder I: conformal case

The nonlinear integral equations describing the spectra of the left and right (continuous) quantum KdV equations on the cylinder are derived from integrable lattice field theories, which turn out to allow the Bethe Ansatz equations of a twisted ``spin -1/2'' chain. A very useful mapping to the more common nonlinear integral equation of the twisted continuous spin $+1/2$ chain is found. The diagonalization of the transfer matrix is performed. The vacua sector is analysed in detail detecting the primary states of the minimal conformal models and giving integral expressions for the eigenvalues of the transfer matrix. Contact with the seminal papers \cite{BLZ, BLZ2} by Bazhanov, Lukyanov and Zamolodchikov is realised. General expressions for the eigenvalues of the infinite-dimensional abelian algebra of local integrals of motion are given and explicitly calculated at the free fermion point.Comment: Journal version: references added and minor corrections performe

Multiparametric quantum gl(2): Lie bialgebras, quantum R-matrices and non-relativistic limits

Multiparametric quantum deformations of $gl(2)$ are studied through a complete classification of $gl(2)$ Lie bialgebra structures. From them, the non-relativistic limit leading to harmonic oscillator Lie bialgebras is implemented by means of a contraction procedure. New quantum deformations of $gl(2)$ together with their associated quantum $R$-matrices are obtained and other known quantizations are recovered and classified. Several connections with integrable models are outlined.Comment: 21 pages, LaTeX. To appear in J. Phys. A. New contents adde

Exact conserved quantities on the cylinder II: off-critical case

With the aim of exploring a massive model corresponding to the perturbation of the conformal model [hep-th/0211094] the nonlinear integral equation for a quantum system consisting of left and right KdV equations coupled on the cylinder is derived from an integrable lattice field theory. The eigenvalues of the energy and of the transfer matrix (and of all the other local integrals of motion) are expressed in terms of the corresponding solutions of the nonlinear integral equation. The analytic and asymptotic behaviours of the transfer matrix are studied and given.Comment: enlarged version before sending to jurnal, second part of hep-th/021109

A braided Yang-Baxter Algebra in a Theory of two coupled Lattice Quantum KdV: algebraic properties and ABA representations

A generalization of the Yang-Baxter algebra is found in quantizing the monodromy matrix of two (m)KdV equations discretized on a space lattice. This braided Yang-Baxter equation still ensures that the transfer matrix generates operators in involution which form the Cartan sub-algebra of the braided quantum group. Representations diagonalizing these operators are described through relying on an easy generalization of Algebraic Bethe Ansatz techniques. The conjecture that this monodromy matrix algebra leads, {\it in the cylinder continuum limit}, to a Perturbed Minimal Conformal Field Theory description is analysed and supported.Comment: Latex file, 46 page

Effects of weight loss and long-term weight maintenance with diets varying in protein and glycemic index on cardiovascular risk factors: the diet, obesity, and genes (DiOGenes) study: a randomized, controlled trial

BACKGROUND: We sought to separately examine the effects of either weight loss or diets varying in protein content and glycemic index without further changes in body weight on cardiovascular risk factors within the Diet, Obesity, and Genes study (DiOGenes). METHODS AND RESULTS: DiOGenes is a pan-European controlled dietary intervention study in 932 overweight adults who first lost body weight on an 8-week low-calorie diet and were then randomized to 1 of 5 ad libitum diets for 26 weeks. The diets were either high or low protein or high or low glycemic index in 4 combinations or control. Weight loss (-11.23 kg; 95% confidence interval, -11.54 to -10.92; P<0.001) reduced high-sensitivity C-reactive protein (-1.15 mg/L; 95% confidence interval, -1.30 to -0.41; P<0.001), low- and high-density lipoprotein cholesterol, triglycerides, and blood pressure. During the 26-week weight maintenance period in the intention-to-treat analysis, the further decrease of high-sensitivity C-reactive protein blood levels was -0.46 mg/L greater (95% confidence interval, -0.79 to -0.13) in the groups assigned to low-glycemic-index diets than in those on high-glycemic-index diets (P<0.001). Groups on low-protein diets achieved a -0.25 mg/L greater reduction in high-sensitivity C-reactive protein (95% confidence interval, -0.59 to -0.17) than those on high-protein diets (P<0.001), whereas lipid profiles and blood pressure were not differently affected. CONCLUSIONS: This large-scale intervention study clearly separates weight loss from dietary composition-related effects. Low-glycemic-index carbohydrates and, to a lesser extent, low-protein intake may specifically reduce low-grade inflammation and associated comorbidities in overweight/obese adults

Supersymmetry and Integrability in Planar Mechanical Systems

We present an N=2-supersymmetric mechanical system whose bosonic sector, with two degrees of freedom, stems from the reduction of an SU(2) Yang-Mills theory with the assumption of spatially homogeneous field configurations and a particular ansatz imposed on the gauge potentials in the dimensional reduction procedure. The Painleve test is adopted to discuss integrability and we focus on the role of supersymmetry and parity invariance in two space dimensions for the attainment of integrable or chaotic models. Our conclusion is that the relationships among the parameters imposed by supersymmetry seem to drastically reduce the number of possibilities for integrable interaction potentials of the mechanical system under consideration.Comment: 20 pages, 3 figure

Fatty acid composition of adipose tissue triglycerides after weight loss and weight maintenance: the DIOGENES study

Fatty acid composition of adipose tissue changes with weight loss. Palmitoleic acid as a possible marker of endogenous lipogenesis or its functions as a lipokine are under debate. Objective was to assess the predictive role of adipose triglycerides fatty acids in weight maintenance in participants of the DIOGENES dietary intervention study. After an 8-week low calorie diet (LCD) subjects with > 8 % weight loss were randomized to 5 ad libitum weight maintenance diets for 6 months: low protein (P)/low glycemic index (GI) (LP/LGI), low P/high GI (LP/HGI), high P/low GI (HP/LGI), high P/high GI (HP/HGI), and a control diet. Fatty acid composition in adipose tissue triglycerides was determined by gas chromatography in 195 subjects before the LCD (baseline), after LCD and weight maintenance. Weight change after the maintenance phase was positively correlated with baseline adipose palmitoleic (16:1n-7), myristoleic (14:1n-5) and trans-palmitoleic acid (16:1n-7t). Negative correlation was found with baseline oleic acid (18:1n-9). Lower baseline monounsaturated fatty acids (14:1n-5, 16:1n-7 and trans 16:1n-7) in adipose tissue triglycerides predict better weight maintenance. Lower oleic acid predicts lower weight decrease. These findings suggest a specific role of monounsaturated fatty acids in weight management and as weight change predictors