RELATIVISTIC HADRONIC MECHANICS - NONUNITARY, AXIOM-PRESERVING COMPLETION OF RELATIVISTIC QUANTUM-MECHANICS

The most majestic scientific achievement of this century in mathematic al beauty, axiomatic consistency, and experimental verifications has b een special relativity with its unitary structure at the operator leve l and canonical structure at the classical level, which has turned out to be exactly valid for point particles moving in the homogeneous and isotropic vacuum (exterior dynamical problems). In recent decades a n umber of authors have studied nonunitary and noncanonical theories, he re generally called deformations, for the representation of broader co nditions, such as extended and deformable particles moving within inho mogeneous and anisotropic physical media (interior dynamical problems) . In this paper we show that nonunitary deformations, including q-, k- , quantum-, Lie-isotopic, Lie-admissible, and other deformations, even though mathematically correct, have a number of problematic aspects o r physical character when formulated on conventional spaces over conve ntional fields, such as lack of invariance of the basic space-time uni ts, ambiguous applicability to measurements, loss of Hermiticity-obser vability in time, lack of invariant numerical predictions, loss of the axions of special relativity, and others. We then show that the class ical noncanonical counterparts of the above nonunitary deformations ar e equally afflicted by corresponding problems of physical consistency. We also show that the contemporary formulation of gravity is afflicte d by similar problematic aspects because Riemannian spaces are noncano nical deformations of Minkowskian spaces, thus having noninvariant spa ce-time units. We then point out that new mathematical methods, called isotopies, genotopies, hyperstructures and their isoduals, offer the possibilities of constructing a nonunitary theory, known as relativist ic hadronic mechanics which: (1) is as axiomatically consistent as rel ativistic quantum mechanics, (2) preserves the abstract axioms of spec ial relativity, and (3) results in a completion of the conventional me chanics much along the celebrated Einstein-Podolski-Rosen argument. A number of novel applications are indicated, such as a geometric unific ation of the special and general relativity via the isominkowskian geo metry in which the two relativities are differentiated via the invaria nt basic unit, while preserving conventional Riemannian metrics. Einst ein's field equations, and related experimental verifications: a novel operator form of gravity verifying the axions of relativistic quantum mechanics under the universal isopoincare symmetry: a new structure m odel of hadrons with conventional massive particles as physical consti tuents which is compatible with composite quarks and with established unitary classifications: and other novel applications in nuclear physi cs, astrophysics, theoretical biology, and other fields. The paper end s with the proposal of a number of new experiments, some of which may imply new practical applications, such as conceivable new forms of rec ycling nuclear waste. The achievement of axiomatic consistency in the study of the above physical problems has been possible for the first t ime in this paper thanks to mathematical advances that recently appear ed in a special issue of the Rendiconti Circolo Matematico Palermo, an d in other journals, identified in the Acknowledgments.