Gauge Transformations in Non-Relativistic Quantum Electrodynamics.

Available from UMI in association with The British Library. Requires signed TDF. This thesis describes a theory of gauge transformations of a quantum electrodynamical Hamiltonian, where the vector and scalar potentials are transformed at the classical Langrangian level and the Hamiltonian is constructed using the usual canonical procedure. The presence of charges is treated non-relativistically in the absence of spin. An hydrogenic atom with an infinitely massive +e charge is first considered. The gauge transforming function is written in terms of the full multi-polar atomic polarisation, governed by three arbitrary parameters. In the dipole approximation and a Coulomb gauge, the transformed Hamiltonian reduces to a simple arbitrary admixture of the usual p cdot A_ {|} and d cdot E_{|} interactions. Various photon transition processes are explicitly demonstrated to be gauge independent. A particular choice of gauge removes the counter-rotating terms and diagonalises the Hamiltonian of a coupled oscillator and a coupled two-level atom. The gauge transformation is generalised to an arbitrary number of charges, each of finite mass, and written in terms of a polarisation measured with respect to an arbitrary atomic centre R^'. It is demonstrated that a complete separation of the interaction into internal atomic and external gross motion components is only possible in a certain gauge, with R^ ' chosen to be the centre of mass. The rates of change of total conjugate and mechanical momenta for the arbitrary charge aggregate are determined within the Heisenberg formalism, demonstrating the importance of the Rontgen interaction term for a complete description of the mechanical effect of radiation. The gauge transformation is further generalised in the last chapter to include longitudinal and scalar radiation fields. A Jaynes-Cummings Hamiltonian in a covariant gauge is constructed by suitable choice of arbitrary parameters.