Chiral Expansion, Renormalization and the Nuclear Force

The renormalization of singular chiral potentials as applied to NN scattering and the structure of the deuteron is discussed. It is shown how zero range theories may be implemented non-perturbatively as constrained from known long range NN forces.Comment: Talk at International IUPAP Conference on Few-Body Problems in Physics (FB18), Santos-Sao Paulo (Brasil), 21-26 August 200

Deuteron radial moments for renormalized chiral potentials

We calculate deuteron positive and negative radial moments involving any bilinear function of the deuteron S and D wave functions for renormalized OPE and TPE chiral potentials. The role played by the strong singularities of the potentials at the origin and the short distance insensitivity of the results when the potentials are fully iterated is emphasized as compared to realistic potentials.Comment: 3 pages, 2 figures. Poster presented at 4th International Conference on Quarks and Nuclear Physics (QNP06), Madrid, Spain, 5-10 Jun 200

Power Counting and Wilsonian Renormalization in Nuclear Effective Field Theory

Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental ---perhaps unknown or unsolvable--- high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.Comment: Contribution to the IJMPE special issue on "Effective Field Theories in Nuclear Physics". This update includes the corrections and changes of the published versio

Statistical Nonlinearities in the Business Cycle

Nonlinear, Real Business Cycles, Efficient Method of Moments

Renormalization Group Analysis of Boundary Conditions in Potential Scattering

We analyze how a short distance boundary condition for the Schrodinger equation must change as a function of the boundary radius by imposing the physical requirement of phase shift independence on the boundary condition. The resulting equation can be interpreted as a variable phase equation of a complementary boundary value problem. We discuss the corresponding infrared fixed points and the perturbative expansion around them generating a short distance modified effective range theory. We also discuss ultraviolet fixed points, limit cycles and attractors with a given fractality which take place for singular attractive potentials at the origin. The scaling behaviour of scattering observables can analytically be determined and is studied with some emphasis on the low energy nucleon-nucleon interaction via singular pion exchange potentials. The generalization to coupled channels is also studied.Comment: 31 pages, 8 figure

Wspieranie pedagogiki demokratycznej? Budżet partycypacyjny w Lizbonie

Social participation is a tool to strengthen peoples’ autonomy and ability to decide upon public issues. It is also an educational and learning tool. In recent times, new forms of social participation have emerged such as the participatory budgets. These foster democratic participation and contribute to more transparent and efficient ways of governing. The participatory budget of Lisbon is an interesting example of municipal social organisation and participation involving learning. The main research question of this article is as follows: how is the participatory budget of Lisbon fostering social learning? Data collected by the use of semi-directed interviews and documental analysis showed that social learning occurred through peoples’ commitment and involvement in local public political issues. However it did not boost the development of an effective democratic participatory experienceU czestnictwo społeczne jest narzędziem wzmacniającym autonomię i zdolność decydowania o kwestiach publicznych. Jest to także narzędzie uczenia innych i uczenia się. W ostatnim czasie pojawiły się nowe formy partycypacji społecznej, takie jak budżety partycypacyjne. Wspierają one demokratyczny udział i przyczyniają się do bardziej przejrzystych i skutecznych sposobów rządzenia. Udział w budżecie w Lizbonie jest interesującym przykładem miejskiej organizacji społecznej i uczestnictwa w takiej edukacji. Główne pytanie badawcze tego artykułu przedstawia się następująco: jak budżet partycypacyjny w Lizbonie wspiera społeczne uczenie się? Dane zebrane przy użyciu częściowo ustrukturyzowanych wywiadów i analizy dokumentacji wykazały, że społeczne uczenie się pojawiło się dzięki zaangażowaniu ludzi w lokalne kwestie polityczne. Nie zwiększyło jednak znacząco doświadczenia w zakresie skuteczności demokratycznego uczestnictwa