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The Aharonov-Casher (AC) phase is calculated in relativistic wave equations of spin one. The AC phase has previously been calculated from the Dirac-Pauli equation using a gauge-like technique \cite{MK1,MK2}. In the spin-one case, we use Kemmer theory (a Dirac-like particle theory) to calculate the phase in a similar manner. However the vector formalism, the Proca theory, is more widely known and used. In the presence of an electromagnetic field, the two theories are `equivalent' and may be transformed into one another. We adapt these transformations to show that the Kemmer theory results apply to the Proca theory. Then we calculate the Aharonov-Casher phase for spin-one particles directly in the Proca formalism.

The Dirac equation in Kerr spacetime is separated using the rotating tetrad formalism. This allows solutions of the Dirac equation, in flat spacetime, written in oblate and prolate spheroidal coordinates to be extracted. The usual MIT bag boundary condition, -i gamma mu nv Psi = Psi is then found to be incompatible with a non-vanishing separated wavefunction except in the spherical limit. However, it is shown that an alternative boundary condition exists that is physically motivated and allows for a non-trivial solution.

The existence of a symmetry of the Dirac equation for a massless particle in a scalar field is demonstrated, and its effect on the bandstructure of certain arrays of scalar delta -function potentials is investigated. The implications of the symmetry for more general scalar potentials are also discussed.

Dirac bispinors may be decomposed into two Weyl spinors with equal modulus Weyl masses. We show from this that in the proper basis, the Lagrangian mass terms for all fundamental fermions can be represented as Weyl mass terms for two two-component Weyl spinors. The natural basis for this decomposition is orthogonal to the natural basis for (charged) fields with gauge symmetry interactions. Implications for sterile neutrinos and flavor physics are examined.

A construction of the Casimir operators of higher degree of the Lie superalgebras osp(1,2n) by a method which represents a generalisation of the method proposed by Micu for the construction of the Casimir operators of the Lie algebras, namely the algebras Sp(2n), is suggested. The method applied has a close connection with Backhouse's method of construction of Casimir operators for the semisimple Lie superalgebras. Above all the fourth-order coefficients of the Casimir operators of superalgebras osp(1,2n) are shown to play a determining role for the Casimir operators of higher degrees.

Studies various manifestations of parity mixing in nuclei in the hope of discriminating between weak interaction theories. It is difficult to reconcile the observed circular polarization of the photon in the reaction n+p to d+ gamma with any of the theories considered here. On the other hand, the observed asymmetry of the 110 keV photon of 19F with respect to the spin direction of the initial state and the circular polarization of the 396 keV photon of 175Lu are consistent with many of the theories, but rule out those which have a strong Delta T=1 part of the weak Hamiltonian. As an important byproduct of our calculations they present evidence that the effective single-particle potential method of calculating parity mixtures is very good approximation to the more accurate two-nucleon potential method.

We study the quantization of the electric charges of the gauge bosons, the Higgs bosons and the fermions in gauge theories. We investigate the intimate relation of the quantization of the electric charge with the spontaneous symmetry breaking, anomaly cancellation and Majorana mass of fermions. We discuss specific examples for the standard model and the SU(5) × U(1)Z model. We find that in these models the electric charges of particles are dynamically quantized.

A many-channel scattering problem with a separable interaction is described and its exact solution is obtained. This solution is then used to discuss various effects in nuclear physics.

The utility of the bremsstrahlung process in detecting parity violations from V-A weak neutral current interference is analysed in two ways. Firstly, bremsstrahlung from polarised-lepton-nucleus scattering has an asymmetry with respect to the polarisation of the incident leptons and, secondly, bremsstrahlung from unpolarised-lepton-nucleus scattering has a small circular polarisation. The magnitude of each effect is calculated. The ratio of the parity-violating contribution and the parity-conserving contribution to the cross section is shown to be a misleading measure of the utility of these experiments. A parameter, the figure of merit, is introduced and used to discuss the feasibility of possible experiments.

At least one massive neutrino, with mass greater than 1 MeV, can provide an explanation of the residual Goldberger-Treiman discrepancy (1938). Agreement with the π → eν branching ratio requires either one massive neutrino with mass between 34 and 139 MeV, or a number of massive neutrinos with appropriately chosen masses and mixing angles.

It is shown that the rho -exchange isovector parity-violating potential is constrained by PCAC to be much weaker than the pi -exchange potential, and much weaker than recently proposed by Galic et al. (1979). This potential does not therefore provide a mechanism for suppressing enhanced neutral-current effects in the pi -exchange potential.