abstract

An explicit colored-graph description of the processes of mass-scattering of Dirac fields in real Minkowski space is used to show how the corresponding twistorial mass-scattering formulae can be entirely derived from a set of simple rules for the graphs. A correspondence between graphs and twistor diagrams is then suggested.

abstract

A two-component spinor form of the conventional electromagnetic Lagrangian density on real Minkowski space is used to obtain the second “half” of Maxwell’s equations from a variational principle. It is shown that a somewhat modified form of the free part of this Lagrangian density can also be employed to derive the explicit equations of motion that give rise to the first “half” of the complete theory. The Penrose expression for the electromagnetic energy-momentum tensor \(T^{ab}(x)\) is explicitly derived by working out a suitable source-free defining relation. The result is that the spinor components associated with \(T^{00}(z)\) and \(T^{0k}(x)\), \(k=1,2,3\), are equal to the ordinary energy and linear-momentum densities of the electromagnetic fields, respectively. A set of explicit kinematical integral expressions for the theory is then exhibited.

abstract

The theory of the quantum Coulomb field associates with each Lorentz frame, i.e., with each unit, future oriented time-like vector \(,\) the operator of the number of transferal infrared photons \(N(u)\) and the phase \(S(u)\) which is the coordinate canonically conjugated with the total charge \(Q: [Q, S(u)]=ie\), \(e\) being the elementary charge. It is shown that the operators \(N(u)\), \((Q/e)S(u)\) and \(Q^2\) form an infinite Lie algebra. One can conclude from this algebra that \(\Delta N(u) = (4/\pi )Q^2\), where \(\Delta \) is the Laplace operator in the Lobachevsky space of four-velocities \(u\), thus relating the total charge \(Q\) with the number of infrared photons.

abstract

We demonstrate in some detail, how an idea of leptons and quarks composed of algebraic partons (defined by a sequence of Clifford algebras) can justify the existence of three and only three families of these fundamental fermions. In this argument, the theory of relativity, the probability interpretation of quantum mechanics and the Pauli exclusion principle, all extended to the algebraic partons, play a crucial role. The Lorentz group turns out to be realisable intrinsically in two different ways, the algebraic partons corresponding to the new way. We describe also a semiempirical mass spectral formula for charged leptons composed of algebraic partons. With the use of experimental \(m_e\) and \(m_{\mu }\) it gives \(m_{\tau } = 1783.47\) MeV or \(m_{\tau } = 1776.80\) MeV, the second option in excellent agreement with new measurements of \(m_{\tau }\).

abstract

We consider polarized protons in the core of a neutron star as the source of the magnetic field. The effective proton magnetic moment is density-dependent and changes sign at some density \(n_r\) and so does the magnetization. Neutron stars with the central density close to \(n_r\) have dipole magnetic field of the order of \(10^{12}\) G. For heavier stars the field decreases fast with the mass, goes through zero and then again increases, albeit in the opposite direction. The abrupt change of the magnetic field occurs on a mass scale of 0.1 solar mass. This model accounts for recent evidence that decay of magnetic field occurs only for neutron stars which accreted matter in their evolution. Conditions are discussed for the polarized proton phase to form the ground state.

abstract

We have found that trapped surfaces due to spherical inhomogeneities can be formed easier in closed universes than in open Friedmann universes. That opens, in principle at least, a new way to resolve the old standing question concerning the openness of the Universe by performing quasi-local experiments.