Relativistic hadronic mechanics of extended deformable particles

A new approach is presented based on (quadratic) transformation theory, for hadronic (Lie-isotopic) generalizations of the Lie-algebraic structures of Heisenberg's equation of motion in nonrelativistic quantum mechanics and the Dirac equation in relativistic quantum mechanics, which are currently used in physical theories of pointlike particles, so as to make them suitable for the description of extended deformable quark-antiquark and three-quark hadron systems without, at the same time, generalizing the physical laws. In nonrelativistic physics (superconductivity), where such a generalization represents the structure of existing theory in the strong-coupling limit, no new result is obtained except insofar as the frequently used analogy between the superconductor and the string model of mesons is elucidated mathematically. The Lie-isotopic and Lie-admissible generalizations of the Lorentz transformation in Einstein's special relativity theory show that the real-time O(3,1) and the imaginary-time O(4) metrics are physically distinguishable, in the sense that interference between the two representations leads to the time asymmetry and rotational asymmetry predicted in the past by Santilli: these asymmetries are images of Einstein's time dilatation and Lorentz contraction in the conventional linear (Lorentz-transformation) theory, in which the O(3,1) and O(4) metrics are indistinguishable