ISOMINKOWSKIAN GEOMETRY FOR THE GRAVITATIONAL TREATMENT OF MATTER ANDITS ISODUAL FOR ANTIMATTER

In a preceding paper at Foundations of Physics Letters,(11) we have su bmitted the apparently first, axiomatically consistent inclusion of gr avitation in unified gauge theories of electroweak interactions under the name of isotopic grand unification. The result was submitted via a n apparent resolution of the structural incompatibilities between elec troweak and gravitational interactions due to: (1) curvature, because the former are defined on a flat spacetime, while the latter are inste ad defined on a curved spacetime; (2) antimatter, because the former c haracterize antimatter via negative-energy solutions, while the latter use instead positive-definite energy-momentum tensors; and (3) basic spacetime symmetries, because the former satisfy the fundamental Poinc are symmetry, which is instead absent for the latter. The main purpose of this paper is to present the methods underlying the isotopic grand unification. We begin with a study of the new mathematics, called iso mathematics, and of the related new geometry, called isominkowskian ge ometry, which permit an apparent resolution of the first incompatibili ty due to curvature. We then pass to a study of the second novel mathe matics, called isodual isomathematics, and related geometry, called is odual isominkowskian geometry, which permit an apparent resolution of the second incompatibility due to antimatter. We then pass to a study of the novel realizations of the conventional Poincare symmetry, known as Poincare-Santilli isosymmetry and its isodual, which provide a uni versal symmetry of gravitation for matter and antimatter, respectively , and permit an apparent resolution of the third incompatibility due t o spacetime symmetries. This paper has been made possible by the prece ding: memoir(5g) recently appeared in Rendiconti Circolo Matematico Pa lermo, which achieves sufficient maturity in the new mathematics; memo ir(4h) recently appeared in Foundations of Physics, which achieves suf ficient maturity in the physical realizations of the new mathematics; and memoir(8c) recently appeared in Mathematical Methods in Applied Sc iences, which achieves sufficient maturity in the formulation of the g eneralized symmetries. Regrettably, in addition to the study of the me thods, we cannot study the novel applications and verifications to pre vent a prohibitive length. Nevertheless, the reader should be aware th at the isominkowskian geometry and its isodual already possess a numbe r of novel applications and experimental verifications in classical ph ysics, particle physics, nuclear physics, astrophysics, gravitation, s uperconductivity, chemistry, antimatter, and biology, which are indica ted in the text with related references without a review.