ISOMINKOWSKIAN GEOMETRY FOR THE GRAVITATIONAL TREATMENT OF MATTER AND ITS ISODUAL FOR ANTIMATTER

Abstract

In a preceding paper at Foundations of Physics Letters,11 we have submitted the apparently first, axiomatically consistent inclusion of gravitation in unified gauge theories of electroweak interactions under the name of isotopic grand unification. The result was submitted via an apparent resolution of the structural incompatibilities between electroweak and gravitational interactions due to: (1) curvature, because the former are defined on a flat spacetime, while the latter are instead defined on a curved spacetime; (2) antimatter, because the former characterize 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 Poincaré 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 isomathematics, and of the related new geometry, called isominkowskian geometry, which permit an apparent resolution of the first incompatibility due to curvature. We then pass to a study of the second novel mathematics, called isodual isomathematics, and related geometry, called isodual 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 Poincaré symmetry, known as Poincaré–Santilli isosymmetry and its isodual, which provide a universal symmetry of gravitation for matter and antimatter, respectively, and permit an apparent resolution of the third incompatibility due to spacetime symmetries. This paper has been made possible by the preceding: memoir5g recently appeared in Rendiconti Circolo Matematico Palermo, which achieves sufficient maturity in the new mathematics; memoir4h recently appeared in Foundations of Physics, which achieves sufficient maturity in the physical realizations of the new mathematics; and memoir8c recently appeared in Mathematical Methods in Applied Sciences, which achieves sufficient maturity in the formulation of the generalized symmetries. Regrettably, in addition to the study of the methods, we cannot study the novel applications and verifications to prevent a prohibitive length. Nevertheless, the reader should be aware that the isominkowskian geometry and its isodual already possess a number of novel applications and experimental verifications in classical physics, particle physics, nuclear physics, astrophysics, gravitation, superconductivity, chemistry, antimatter, and biology, which are indicated in the text with related references without a review.