Abstract:
We assume a triple geometric structure for the electromagnetic nuclear interaction. This nuclear electromagnetism is used to calculate the binding energies of the alpha particle and the A=3 isobar nuclides. The approximation for the resultant wave equation which lead to the deuteron binding energy from the modified Mathieu equation for the radial eigenvalue equation also establishes proton-electron-proton magnetic bonds in these nuclides and determines their binding energies. Completely theoretical calculations give 28.5 Mev., 7.64 Mev. and 8.42 Mev. for the binding energies of the alpha particle, the helium 3 isotope and tritium respectively. These values admit correction factors due to the approximations made.

Abstract:
The lepton mass ratios are calculated using a geometric unified theory, taking the leptons as the only three possible families of topological excitations of the electron or the neutrino. The theoretical results give 107.5916 Mev for the muon mass and 1770.3 Mev for the tau mass using the mass ratios. Using the additional geometric interaction energy in a muon-neutrino system, the main leptonic mass contribution to the pion and kaon mass is calculated to be, respectively, 140.88 Mev and 494.76 Mev. The necessary first order corrections, due to the interaction of the excitations, should be of the order of the discrepancies with experimental values. The three geometric families of leptonic excitations may be related to a quark structure.

Abstract:
It is shown that geometric connection field excitations acquire mass terms from a geometric background substratum related to the structure of space-time. Commutation relations in the electromagnetic su(2) sector of the connection limit the number of possible masses. Calculated results, within corrections of order alpha, are very close to the experimental masses of the intermediate W, Z bosons.

Abstract:
We assume a triple geometric structure for the electromagnetic nuclear interaction. This nuclear electromagnetism is used to calculate the binding energies of the deuteron and the neutron. The corresponding Pauli quantum wave equation in a geometric theory, with the SU(2) electromagnetic coupling instead of the standard "minimal" coupling, contains a 1/r to-the-fourth-power, short-range attractive magnetic potential term. This term, produced by the odd part of the electromagnetic potential, may be responsible for a strong nuclear interaction. An approximation for the resultant wave equation leads to the modified Mathieu equation. Completely theoretical calculations give 2.205 Mev, 0.782 Mev and 27.6 Mev for the binding energies of the deuteron, the neutron and the alpha particle respectively. These values admit correction factors due to the approximations made.

Abstract:
In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for empty space. For non empty space we obtain a generalized Einstein equation, relating the Einstein tensor to a geometric stress energy tensor. The matching exterior solution is in agreement with the standard relativity tests. Furthermore, there is a Newtonian limit where we obtain Poisson's equation.

Abstract:
Geometric interactions in a new relativistic geometric unified theory include interactions other than gravitation and electromagnetism. In a low energy limit one of these interactions leads essentially to a Fermi type theory of weak interactions including the Hamiltonian and coupling constant.

Abstract:
Geometric relativistc interactions in a new geometric unified theory are classified using the dynamic holonomy groups of the connection. Physical meaning may be given to these interactions if the frame excitations represent particles. These excitations have algebraic and topological quantum numbers. The proton, electron and neutrino may be associated to the frame excitations of the three dynamical holonomy subgroups. In particular, the proton excitation has a dual mathematical structure of a triplet of subexcitations. Hadronic, leptonic and gravitational interactions correspond to the same subgroups. The background geometry determines non trivial fiber bundles where excitations live, introducing topological quantum numbers that classify families of excitations. From these three particles, the only stable ones, it may be possible, as suggested by Barut, to build the rest of the particles. The combinations of the three fundamental excitations display SU(3)xSU(2)xU(1) symmetries.

Abstract:
A previously proposed geometric definition of mass in terms of energy, in a geometrical unified theory, is used to obtain a numerical expression for a ratio of masses of geometrical excitations. The resultant geometric ratio is approximately equal the ratio of the proton to electron physical masses.

Abstract:
Excitations of a relativistic geometry are used to represent the theory of quantum electrodynamics. The connection excitations and the frame excitations reduce, respectively, to the electromagnetic field operator and electron field operator. Because of the inherent geometric algebraic structure these operators obey the standard commutation rules of QED. If we work with excitations, we need to use statistical theory when considering the evolution of microscopic subsystems. The use of classical statistics, in particular techniques of irreversible thermodynamics, determine that the probability of absorption or emission of a geometric excitation is a function of the classical energy density. Emission and absorption of geometric excitations imply discrete changes of certain physical variables, but with a probability determined by its wave energy density. Hence, this geometric theory, without contradicting the fundamental aspects of quantum physics, provides a geometric foundation for the theory.

Abstract:
The value of the alpha constant, known to be equal to an algebraic expression in terms of pi and entire numbers related to certain group volumes, is derived from the relativistic structure group of a geometric unified theory, its subgroups and corresponding symmetric space quotients.