Articles written in Proceedings – Section A
Volume 21 Issue 4 April 1945 pp 135-146
The classical formulæ for the scattering of scalar mesons by a neutron are obtained taking account of the radiation damping. The neutron is assumed to possess a ‘charge’ and a ‘dipole moment’. The scattering due to each of these is treated separately. It is found that the formulæ for the scattering due to the dipole has exactly the same form as the one obtained by Bhabha for the transverse mesons. Due to numerical factors the scattering for large energies of the incident mesons is double, and for small energies half that of transverse vector-mesons.
The scalar and pseudo-scalar charge and dipole interactions are considered in the quantum theory. The scalar dipole interaction does not give rise to any scattering at all, the whole of the scattering being due to the pseudo-scalar interaction. In this case the quantum-theoretical formulæ agree with the corresponding classical ones if the effect of radiation reaction is neglected in the latter.
Volume 22 Issue 1 July 1945 pp 30-41
The Dirac-matrices generate an algebra consisting of sixteen linearly independent elements. A formula is given for expressing the product of any two elements as a linear combination of these sixteen. This determines the structure of the algebra completely. It is shown that certain known identities concerning these matrices can be obtained comparatively casily by the present method. Some new identifies are also deduced.
The characteristic equation of a general element of the algebra is derived and from it an expression is obtained for the determinant of any four-dimensional matrix representing the element. This expression is used to discuss the case of a particle of spin 1/2 having an explicit spin interaction with the electromagnetic field. It is shown that in the classical limit
Volume 23 Issue 3 March 1946 pp 152-163