Elementary Particles in the Generalized Theory of Gravitation

Abstract

This paper contains, for the time independent spherically symmetric fields, various regular solutions of the field equations. An elementary particle structure consists of the entire spectrum of magnetic charges g_n, n=0,1,2,..., with alternating signs where g_n → 0 for n → ∞ and where $\sum\limits_{n=0}^{\infty }{{{g}_{n}}}=0$. The screening caused by the stratified distribution generates short range magnetic forces. The strength of the coupling between the field and particle is described by e²+g ²_n where n=∞ corresponds to the distances of the order of a Compton wave length $\frac{\hbar }{Mc}$Mc. The observed mass M of particle or antiparticle is obtained, as a consequence of the equations of motion, in the form Mc² = ½ mc² +2E_s, where E_s is the finite selfenergy of particle (or antiparticle) and where m and E_s have opposite signs. The “bare gravitational mass” m, obtained as a constant of integration, is estimated to be of the order of 10²¹ Mev. The spectrum of fundamental lengths r_on [= $\frac{/\left( 2{{G}_{o}} \right)}{{{c}^{2}}}/\left( {{e}^{2}}+\mathop{g}_{n}^{2} \right)$ ~ 10⁻³³cm] measure the deviation of the theory from general relativity. The selfenergy E_s in the limit r_on = 0 tends to infinity and the solutions reduce to the corresponding spherically symmetric solutions in general relativity. The spin ½ of an elementary particle is found to be the result of its neutral magnetic structure and the latter exists only for nonvanishing Γ ^ρ_[μν] , the antisymmetric part of the affine connection. The two states of spin correlate with the two possible sequences of signs of g_n, i.e g_n and — g_n, n=0,1,2,.... .

For the solutions where e=0 the symmetries of charge conjugation and parity are not conserved. The latter lead to the assumption of small masses for the two neutrinos ν_e, ν_μ. Conservation of the electric charge multiplicity i.e the existence of −1, +1, 0 units of electric charge, is found to be the basis for the existence of four massive fundamental particles p,e,ν_e,ν_μ and the corresponding antiparticles $\overset{-}{\mathop p}\,,{{e}^{+}},\overset{-}{\mathop {{\nu }_{e}}}\,,\overset{-}{\mathop {{\nu }_{\mu }}}\,$p. Based on a new concept of “vacuum” predicted by the theory it may be possible to construct all other elementary particles as bound or resonance states of the “fundamental quartet” p,e,ν_e,ν_μ and the “antiquartet” $\overset{-}{\mathop p}\,,{{e}^{+}},\overset{-}{\mathop {{\nu }_{e}}}\,,\overset{-}{\mathop {{\nu }_{\mu }}}\,$.