Renormalization programme for effective theories

We summarize our latest developments in perturbative treating the effective theories of strong interactions. We discuss the principles of constructing the mathematically correct expressions for the S-matrix elements at a given loop order and briefly review the renormalization procedure. This talk shall provide the philosophical basement as well as serve as an introduction for the material presented at this conference by A. Vereshagin and K. Semenov-Tian-Shansky.Comment: 6 pages, talk given at HSQCD 2004, Russia, May 2004, to be published in Proceeding

Bootstrap and the Parameters of Pion-Nucleon Resonances

In this talk we demonstrate the results of application of the perturbative effective theory formalism developed in recent papers to the calculation of $\pi N$ elastic scattering amplitude. Restrictions on the contributing resonance parameters are obtained and the low energy coefficients are calculated.Comment: 6 pages, talk given at the X. International Conference On Hadron Spectroscopy (HADRON'03), August 31 - September 6, 2003, Aschaffenburg, Germany; to appear in Proceeding

Bootstrap and the physical values of πN\pi N resonance parameters

This is the 6th paper in the series developing the formalism to manage the effective scattering theory of strong interactions. Relying on the theoretical scheme suggested in our previous publications we concentrate here on the practical aspect and apply our technique to the elastic pion-nucleon scattering amplitude. We test numerically the pion-nucleon spectrum sum rules that follow from the tree level bootstrap constraints. We show how these constraints can be used to estimate the tensor and vector $NN\rho$ coupling constants. At last, we demonstrate that the tree-level low energy expansion coefficients computed in the framework of our approach show nice agreement with known experimental data. These results allow us to claim that the extended perturbation scheme is quite reasonable from the computational point of view.Comment: 41 pages, 7 figure

Localizable Effective Theories, Bootstrap and the Parameters of Hadron Resonances

We discuss the basic principles of constructing a meaningful perturbative scheme for effective theory. The main goal of this talk is to explain the approach and to present recent results obtained with the help of the method of Cauchy forms in several complex variables.Comment: 6 pages, Talk given at the X. International Conference On Hadron spectroscopy (HADRON'03), August 31 - September 6, 2003, Aschaffenburg, Germany; to appear in Proceeding

The resultant parameters of effective theory

This is the 4-th paper in the series devoted to a systematic study of the problem of mathematically correct formulation of the rules needed to manage an effective field theory. Here we consider the problem of constructing the full set of essential parameters in the case of the most general effective scattering theory containing no massless particles with spin J > 1/2. We perform the detailed classification of combinations of the Hamiltonian coupling constants and select those which appear in the expressions for renormalized S-matrix elements at a given loop order.Comment: 21 pages, 4 LaTeX figures, submitted to Phys. Rev.