Heisenberg Honeycombs Solve Veneziano Puzzle

摘要: In this (expository) paper and its (more technical) companion we reformulate some results of the Nobel Prize winning by Werner Heisenberg into modern mathematical language honeycombs. This was recently developed in connection with complete solution Horn problem (to be defined explained text). Such a reformulation is done purpose posing solving following problem: analyzing (spectroscopic) experimental data it possible to recreate underlying microscopic model generating these data? Although case Hydrogen atom positive answer known, obtain an affirmative for spectra other quantum mechanical systems much harder task. Development Heisenberg’s ideas happens most useful purpose. It supplies needed tools solve Veneziano puzzles. The meaning word ”puzzle” two-fold. On one hand, means (in amplitudes) find physical reproducing amplitudes. another, from point view combinatorics honeycombs, explicitly fusion rules such Solution tasks facilitated our earlier string-theoretic formalism. only qualitative arguments are presented (with few exceptions). These provide enough evidence that compatible amplitudes standard (i.e. non supersymmetric!) QCD. addition, usefulness proposed formalism illustrated on numerous examples as physically motivated saturation conjecture text), derivation Yang-Baxter Knizhnik-Zamolodchikov equations,Verlinde Hecke algebras, computation Gromov-Witten invariants small cohomology ring, etc. Finally, discuss uses condensed matter physics