A Calogeracos
The interaction of a fast moving sine-Gordon soliton with an external periodic potential is examined. The resulting equation of motion for the collective coordinate representing the position of the soliton is given in relativistic form. We…
We address the question of radiation emission from both perfect and dispersive mirrors following prescribed relativistic trajectories. The trajectories considered are asymptotically inertial: the mirror starts from rest and eventually…
The early papers by Klein, Sauter and Hund which investigate scattering off a high step potential in the context of the Dirac equation are discussed to derive the 'paradox' first obtained by Klein. The explanation of this effect in terms of…
We investigate a commonly used formula which seems to give non-integral vacuum charge in the continuum limit. We show that the limit is subtle and care must be taken to get correct results.
The Klein paradox is reassessed by considering the properties of a finite square well or barrier in the Dirac equation. It is shown that spontaneous positron emission occurs for a well if the potential is strong enough. The vacuum charge…
It is shown that a Dirac particle of mass $m$ and arbitrarily small momentum will tunnel without reflection through a potential barrier $V=U_c(x)$ of finite range provided that the potential well $V=-U_c(x)$ supports a bound state of energy…
A second quantised theory of electrons and positrons in a deep time-dependent potential well is discussed. It is shown that positron production from the well is a natural consequence of Dirac's hole theory when the strength of the well…