Alien Calculus and non perturbative effects in Quantum Field Theory

In many domains of physics, methods are needed to deal with non-perturbative aspects. I want here to argue that a good approach is to work on the Borel transforms of the quantities of interest, the singularities of which give non-perturbative contributions. These singularities in many cases can be largely determined by using the alien calculus developed by Jean \'Ecalle. My main example will be the two point function of a massless theory given as a solution of a renormalization group equation.Comment: 4 pages, double-colum

An Efficient Method for the Solution of Schwinger--Dyson equations for propagators

Efficient computation methods are devised for the perturbative solution of Schwinger--Dyson equations for propagators. We show how a simple computation allows to obtain the dominant contribution in the sum of many parts of previous computations. This allows for an easy study of the asymptotic behavior of the perturbative series. In the cases of the four-dimensional supersymmetric Wess--Zumino model and the $\phi_6^3$ complex scalar field, the singularities of the Borel transform for both positive and negative values of the parameter are obtained and compared.Comment: 9 pages, no figures. Match of the published version, with the corrections in proo

Demand and Supply of Crop Infraspecific Diversity on Farms: Towards a Policy Framework for On-Farm Conservation

Interest is increasing worldwide in on-farm conservation as a component of a strategy to conserve crop genetic resources. On-farm conservation may require outside support to small-scale farmers in areas of crop domestication and diversity. This paper argues that crop infraspecific diversity maintained by farming households in these areas results from the interplay between demand and supply for this diversity (i.e., its loss may be demand- or supply-related). In the first instance, interventions should be aimed at increasing the value of crop diversity for farmers or decreasing the farm-level opportunity costs of maintaining diversity. In the second instance, interventions should decrease the transaction costs of accessing crop diversity. It may be difficult, however, to distinguish in empirical research, whether the constraints to diversity are demand- or supply-related. Therefore the process of supporting on-farm conservation should be kept as open as possible and both demand and supply interventions should be available.Crop Production/Industries,

Conventionalisation? Organic farming bites back!

This is a summary of the discussion during the workshop 2.6 on conventionalisation of organic farming and how farmers or farmers' associations avoid conventionalisation. It also includes the abstracts of the papers that were presented during the workshop

The quantum Neumann model: asymptotic analysis

We use semi--classical and perturbation methods to establish the quantum theory of the Neumann model, and explain the features observed in previous numerical computations.Comment: 14 pages, 3 figure

The quantum Neumann model: refined semiclassical results

We extend the semiclassical study of the Neumann model down to the deep quantum regime. A detailed study of connection formulae at the turning points allows to get good matching with the exact results for the whole range of parameters.Comment: 10 pages, 5 figures Minor edit

A comment on free-fermion conditions for lattice models in two and more dimensions

We analyze free-fermion conditions on vertex models. We show --by examining examples of vertex models on square, triangular, and cubic lattices-- how they amount to degeneration conditions for known symmetries of the Boltzmann weights, and propose a general scheme for such a process in two and more dimensions.Comment: 12 pages, plain Late

Singularity, complexity, and quasi--integrability of rational mappings

We investigate global properties of the mappings entering the description of symmetries of integrable spin and vertex models, by exploiting their nature of birational transformations of projective spaces. We give an algorithmic analysis of the structure of invariants of such mappings. We discuss some characteristic conditions for their (quasi)--integrability, and in particular its links with their singularities (in the 2--plane). Finally, we describe some of their properties {\it qua\/} dynamical systems, making contact with Arnol'd's notion of complexity, and exemplify remarkable behaviours.Comment: Latex file. 17 pages. To appear in CM

On the icosahedron: from two to three dimensions

In his famous book, Felix Klein describes a complex variable for the quotients of the ordinary sphere by the finite groups of rotations and in particular for the most complex situation of the quotient by the symmetry group of the icosahedron. The purpose of this work and its sequels is to obtain similar results for the quotients of the three--dimensional sphere. Various properties of the group $SU(2)$ and of its representations are used to obtain explicit expressions for coordinates and the relations they satisfy.Comment: 8 page