The The Fine Structure Constant and Radiative Corrections for the Electron and Positron Cores as Viewed in the Planck Vacuum Theory

The present paper derives the radiative corrections for the electron and positron cores in the Planck vacuum theory, leading to the electron and position particles in a 7-dimension spacetime. The physical meaning of the fine structure constant is twofold: it is the ratio of the electron spin coefficient to the electron-core spin coefficient; and it is the probability that an electron or positron will emit or absorb a photon. The nature of this photon defines the spin quanta in the PV theory. Results suggest that the Feynman and Schwinger QED calculations refer to the PV state. Finally, the closed-loop electron-positron pairs in the Feynman diagrams are explained.

NEUTRINO ASYMMETRY IN GENERAL RELATIVISTIC ROTATING RADIATIVE STARS

Neutrino asymmetry in general relativistic radiative spacetime exterior to spinning stars is investigating by making use of Newman–Penrose (NP) spin coefficient formalism. It is shown that neutrino current depends on the direction of rotation of the star. The solution is obtained in test field approximation where the neutrinos do not generate gravitational fields.

SPACE–TIMES WITH A TWO-DIMENSIONAL GROUP OF CONFORMAL MOTIONS

The necessary and sufficient conditions for a space–time to admit a two-dimensional group of conformal motions (and, in particular, of homothetic motions) acting on nonnull orbits are found in the compacted spin-coefficient formalism. Although the discussion is restricted to the case of spacelike orbits, similar results are readily obtained for timelike orbits via the (modified) Sachs star operation. A number of theorems are obtained dealing with such topics as the Gaussian curvature of the group orbits, orthogonal transitivity, and hypersurface orthogonality of the conformal Killing vectors. A simple proof is presented of a generalization of a theorem due to Papapetrou.

Some solutions of the Lanczos vacuum wave equation

In general relativity the non-local part of the gravitational field is described by the 10 degrees of freedom of the Weyl conformal curvature tensor C abcd . In every space-time the Weyl field C abcd is derivable from a potential L abc which has at most 16 algebraically independent components reducing to 10 degrees of freedom when the six gauge conditions L ab s ; s = 0 are imposed. The potential L abc discov­ered by Lanczos was shown by Illge to have an extremely simple vacuum wave equation, namely, □ L abc ≡ g sm L abc ; s ; m = 0. Using tensor, spinor and spin-coefficient methods we give some solutions of this new vacuum wave equation in some spacetimes containing one or more preferred vector fields.