Outline of Hadronic Mathematics, Mechanics and Chemistry as Conceived by R. M. Santilli

Abstract

In this paper, we outline the various branches of hadronic mathematics and their applications to corresponding branches of hadronic mechanics and chemistry as conceived by the Italian-American scientist Ruggero Maria Santilli. According to said conception, hadronic mathematics comprises the following branches for the treatment of matter in conditions of increasing complexity: 1) 20th century mathematics based on Lie’s theory; 2) IsoMathematics based on Santilli’s isotopies of Lie’s theory; 3) GenoMathematics based on Santilli’s formulation of Albert’s Lie-admissibility; 4) HyperMathematics based on a multi-valued realization of genomathematics with classical operations; and 5) HyperMathematics based on Vougiouklis Hv hyperstructures expressed in terms of hyperoperations. Additionally, hadronic mathematics comprises the anti-Hermitean images (called isoduals) of the five preceding mathematics for the description of antimatter also in conditions of increasing complexity. The outline presented in this paper includes the identification of represented physical or chemical systems, the main mathematical structure, and the main dynamical equations per each branch. We also show the axiomatic consistency of various branches of hadronic mathematics as sequential coverings of 20th century mathematics; and indicate a number of open mathematical problems. Novel physical and chemical applications permitted by hadronic mathematics are presented in subsequent collections.