The multivariate signed Bollobas-Riordan polynomial

We generalise the signed Bollobas-Riordan polynomial of S. Chmutov and I. Pak [Moscow Math. J. 7 (2007), no. 3, 409-418] to a multivariate signed polynomial Z and study its properties. We prove the invariance of Z under the recently defined partial duality of S. Chmutov [J. Combinatorial Theory, Ser. B, 99 (3): 617-638, 2009] and show that the duality transformation of the multivariate Tutte polynomial is a direct consequence of it.Comment: 17 pages, 2 figures. Published version: a section added about the quasi-tree expansion of the multivariate Bollobas-Riordan polynomia

On the Effective Action of Noncommutative Yang-Mills Theory

We compute here the Yang-Mills effective action on Moyal space by integrating over the scalar fields in a noncommutative scalar field theory with harmonic term, minimally coupled to an external gauge potential. We also explain the special regularisation scheme chosen here and give some links to the Schwinger parametric representation. Finally, we discuss the results obtained: a noncommutative possibly renormalisable Yang-Mills theory.Comment: 19 pages, 6 figures. At the occasion of the "International Conference on Noncommutative Geometry and Physics", April 2007, Orsay (France). To appear in J. Phys. Conf. Se

Optomechanical tailoring of quantum fluctuations

We propose the use of feedback mechanism to control the level of quantum noise in a radiation field emerging from a pendular Fabry-Perot cavity. It is based on the possibility to perform quantum nondemolition measurements by means of optomechanical coupling.Comment: ReVTeX file, 8 pages, 1 Postscript figure. to appear in J. Opt. B: Quant. Semiclass. Op

Constructive Matrix Theory

We extend the technique of constructive expansions to compute the connected functions of matrix models in a uniform way as the size of the matrix increases. This provides the main missing ingredient for a non-perturbative construction of the $\phi^{\star 4}_4$ field theory on the Moyal four dimensional space.Comment: 12 pages, 3 figure

Noncommutative Induced Gauge Theories on Moyal Spaces

Noncommutative field theories on Moyal spaces can be conveniently handled within a framework of noncommutative geometry. Several renormalisable matter field theories that are now identified are briefly reviewed. The construction of renormalisable gauge theories on these noncommutative Moyal spaces, which remains so far a challenging problem, is then closely examined. The computation in 4-D of the one-loop effective gauge theory generated from the integration over a scalar field appearing in a renormalisable theory minimally coupled to an external gauge potential is presented. The gauge invariant effective action is found to involve, beyond the expected noncommutative version of the pure Yang-Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic term, which for the noncommutative $\phi^4$-theory on Moyal space ensures renormalisability. A class of possible candidates for renormalisable gauge theory actions defined on Moyal space is presented and discussed.Comment: 24 pages, 6 figures. Talk given at the "International Conference on Noncommutative Geometry and Physics", April 2007, Orsay (France). References updated. To appear in J. Phys. Conf. Se

Energy Densities of Brown Trout (Salmo trutta) and Its Main Prey Items in an Alpine Stream of the Slizza Basin (Northwest Italy)

ABSTRACT In the present study, energy densities of 80 adult brown trout (Salmo trutta), seasonally sampled in an alpine stream in the eastern Alps and energy densities of their main prey items, were determined. The energy density (J/g wet mass) and dry weight content (%) of fish were highly correlated (p<0.00 1) and averaged 5, 611.6 ± 857.9 J/g wet mass and 25.3 ± 2.1% dry weight, respectively. Energy density values were significantly higher in fish sampled in spring than in other seasons. No major changes in the energy content were observed due to age or sex. Macroinvertebrates. particularly Ephemeroptera and Diptera, were the major food source of brown trout in the sampled area. Their gross energy content varied within a wide range of values (1, 654–5, 110 J/g wet weight), depending on the taxa and family or genus within a given taxon

Renormalization of the commutative scalar theory with harmonic term to all orders

The noncommutative scalar theory with harmonic term (on the Moyal space) has a vanishing beta function. In this paper, we prove the renormalizability of the commutative scalar field theory with harmonic term to all orders by using multiscale analysis in the momentum space. Then, we consider and compute its one-loop beta function, as well as the one on the degenerate Moyal space. We can finally compare both to the vanishing beta function of the theory with harmonic term on the Moyal space.Comment: 16 page

One-loop Beta Functions for the Orientable Non-commutative Gross-Neveu Model

We compute at the one-loop order the beta-functions for a renormalisable non-commutative analog of the Gross Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this non-commutative field theory exhibits asymptotic freedom for any number of colors. The beta-function for the non-commutative counterpart of the Thirring model is found to be non vanishing.Comment: 16 pages, 9 figure

Renormalization of the Orientable Non-commutative Gross-Neveu Model

We prove that the non-commutative Gross-Neveu model on the two-dimensional Moyal plane is renormalizable to all orders. Despite a remaining UV/IR mixing, renormalizability can be achieved. However, in the massive case, this forces us to introduce an additional counterterm of the form "psibar i gamma^{0} gamma^{1} psi". The massless case is renormalizable without such an addition.Comment: 45 pages, 5 figure