St-Petersburg State University Research Institute of Physics Faculty of Physics High Energy and Elementary Particles Physics
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1. Some previously discussed results (brief reminder).

   1a. Cauchy forms in hyperlayers for a polynomially bounded
       meromorphic function of two complex variables.
   1b. Bootstrap conditions of the first and second kind.
       Examples for the string-like (Lovelace) amplitude.
   1c. Bootstrap conditions and the constructive field-theoretic
       form of Veneziano's duality hypothesis.

2. How to assign meaning to the tree-level approximation of the extended
   perturbation scheme of effective scattering theory of strongly
   interacting scalar particles:

   2a. The reduction procedure and classification of S-matrix parameters.
   2b. The system of Feynman rules in terms of tree-level minimal
   2c. Pole structure of the tree-level amplitude of binary scattering
   2d. Two basic principles: summability and uniformity. Cauchy forms for
       the tree-level 4-leg amplitude in three intersecting hyperlayers.

3. Bootstrap conditions and renormalization prescriptions fixing the
   4-leg tree-level minimal vertex.

4. Additional constrains for the allowed set of renormalization
   prescriptions that fix 3-leg minimal tree-level vertices.

5. Numerical tests of sum rules that follow from the bootstrap system.
   5a. Numerical test in a toy bootstrap model for string-like amplitude.
   5b. Numerical test of sum rules for pion-nucleon spectrum parameters

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March 2009