Table of contents

A consistent scheme of quantum electrodynamics with auxiliary fields of photons and electrons of infinitely large masses is developed. The auxiliary fields are introduced from the very beginning in the Lagrangian density, but it is ensured by means of suitable initial conditions that these fields are completely unobservable. For some of the auxiliary photon fields the usual sign of the Lagrangian density is reversed, while for some of the auxiliary electrons fields the usual statistics of the field is reversed. For such fields it is found necessary to use an indefinite metric.

It is shown that the present treatment provides us with a well-defined procedure for the evaluation of divergent integrals in quantum electrodynamcs. As an application, the self-energy of the photon is evaluated and shown to vanish for a free photon.

The importance of the coulomb forces in mixing states with a different isotopic spin T is investigated assuming charge independence of the specific nuclear forces. It is found that for two and four nucleons outside a closed shell in the state T=0 this mixing is very small (less than 0.25%, taking into account interconfigurational mixing). It can therefore be concluded that the coulomb forces have very little importance in destroying the validity of the isotopic spin selection rules for β and γ transitions and for collisions, which result from the assumption of the charge independence of nuclear forces.

Certain exact solutions of the field equations of general relativity for empty space containing an electrostatic field are derived, and a physical interpretation is attempted. The canonical cylinder coordinates of Weyl are used, and all the solutions in which the electrostatic potential depends on only one of the two variables are obtained. Some of these are special cases of a class of solutions previously obtained by Weyl and they are shown to correspond either to a uniform electric field or to the field of a line-charge. Two of the solutions are not members of Weyl's class, and in these the electric field has no analogue in classical electrostatics and possesses the property of generating an orthogonal gravitational field.

The statistical aspect of the second law of thermodynamics is illustrated by a discussion of two simple models. In both cases the most probable behaviour, and the mean life and the average time of recurrence of different states of fluctuation are obtained and discussed.

An anticoincidence counter arrangement showed no significant asymmetry in the arrival of moderate-energy neutrons at sea level. It is concluded that these neutrons do not maintain the same direction as the primary cosmic-ray particles which give rise to them.

An experimental study by the powder deposit technique has been made of interesting domains of reverse magnetization which arise when an initially saturated crystal of silicon-iron is demagnetized. Two cases have been studied with the crystal (a) as perfect as possible, and (b) with an artificial defect made at one end to provide controlled demagnetization effects. They show that imperfections in the surface are very important in determining the observed demagnetization phenomena. The surfaces of the crystal may themselves act as imperfections.

The most probable specific ionization of energetic μ-mesons has been measured as a function of momentum, using proportional counters filled with a neonmethane mixture. The results confirm previous measurements, and are in good agreement with the theoretically predicted increase of specific ionization at high momenta.

The cross sections for resonance electron capture from hydrogen atoms by protons of incident energy up to 100 keV are calculated theoretically using the Perturbed Stationary State method and a comparison is made with the results of the Born approximation both with and without neglect of momentum transfer.

A new modification of the Thomas-Fermi formula is derived which is similar to Weizsäcker's; this provides what is claimed to be a more plausible proof than usual of the Thomas-Fermi method. The method is applied to give a non-divergent relativistic approximation for Z<137/2 and is used to demonstrate the incorrectness of the Thomas-Fermi-Dirac equation based on Foch's equations. Slater's approximation to Foch's equations is used to derive a Thomas-Fermi equation with exchange only differing from Dirac's by a change in Z. The solutions of this equation are re-interpreted and shown to be not unique, though always giving a positive electron density.