Isotopic lifting of analytic and quantum mechanics - Santilli, Ruggero María (Rev. Téc. Fac. Ing. Univ. Zulia)
In a preceding article we have introduced the isotopies of the differential calculus and of Newton’s equations of motion. In this second paper we use these results lo construct the isotopies of analytic and quantum mechanics. We show that the isotopies of Hamiltonian mechanics permit the derivation from a first-order isovariational principie of the most general possiblenonlinear integro-differential Newton’s equations by providing in particular a representation of the extended and deformable shape of the body considered as well as of nonlocal-integral and variationally non-self-adjoint forces. We then identify the isotopies of conventional quantization and show that they lead lo unique and unambiguous isotopies of quantum mechanics capable of preserving all the essential characteristics of the original isotopic Newton’s equations, thus permitting the representation in the fixed inertial frame of the experimenter of nonlinear, nonlocal and nonhamiltonian systems, with considerable broadening of the arena of applicability of conventional formulations.