The Strong Levinson Theorem for the Dirac Equation

We consider the Dirac equation in one space dimension in the presence of a symmetric potential well. We connect the scattering phase shifts at E=+m and E=-m to the number of states that have left the positive energy continuum or joined the negative energy continuum respectively as the potential is turned on from zero.Comment: Submitted to Physical Review Letter

Klein Tunnelling and the Klein Paradox

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 and lifetime of the well are estimated. If the well is wide enough, a seemingly constant current is emitted. These phenomena are transient whereas the tunnelling first calculated by Klein is time-independent. Klein tunnelling is a property of relativistic wave equations, not necessarily connected to particle emission. The Coulomb potential is investigated in this context: it is shown that a heavy nucleus of sufficiently large $Z$ will bind positrons. Correspondingly, it is expected that as $Z$ increases the Coulomb barrier will become increasingly transparent to positrons. This is an example of Klein tunnelling.Comment: 17 page

Fermionic Bound States and Pseudoscalar Exchange

We discuss the possibility that fermions bind due to Higgs or pseudoscalar exchange. It is reasonable to believe on qualitative grounds that this can occur for fermions with a mass larger than 800-900 GeV. An exchange of a pseudoscalar boson leads in the non-relativistic limit to an unacceptable potential which behaves like 1/r^3 at the origin. We show that this singular behaviour is smeared out when relativistic effects are included

Polarisation observables in lepton antilepton to proton antiproton reactions including lepton mass

General expressions, including the lepton mass, for the spin averaged differential cross section for the annihilation reaction lepton antilepton to proton antiproton are given, as well as general formulae for the single and double spin asymmetries in the centre of mass frame. In particular we discuss the single spin asymmetry, normal to the scattering plane, which measures the relative phase difference between nucleon electromagnetic form factors $G_E$ and $G_M$. Recent experimental investigations of these form factors in the space and time like region are reviewed. It is thought that measurements of the phase of these form factors will provide fundamental information on the internal nucleon structure. The phases between $G_E$ and $G_M$ are accessible through polarisation observables measured in the antiproton proton to lepton antilepton reaction, or in its time reversed process.Comment: 14 pages, to be submitted to EPJ

Threshold Behaviour in Gauge Boson Pair Production at LEP 2

We discuss the form of the amplitude for gauge boson pair production at or near threshold.We show that in the case of W-pair production at LEP2 near threshold only one anomalous electromagnetic coupling can contribute. This anomalous coupling is CP violating and contributes to the electric dipole moment of the $W$. Since this coupling is likely to be small, it is important to look for ZZgamma couplings in Zgamma production. These couplings are not suppressed at the W-threshold

The Continuum Limit and Integral Vacuum Charge

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.Comment: 5 pages. Submitted to JETP Letter

Transmission resonances and supercritical states in a one dimensional cusp potential

We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric cusp potential. We compute the scattering and bound states solutions and we derive the conditions for transmission resonances as well as for supercriticality.Comment: 10 pages. Revtex 4. To appear in Phys Rev.

Radiative Correction to the Transferred Polarization in Elastic Electron-Proton Scattering

Model independent radiative correction to the recoil proton polarization for the elastic electron-proton scattering is calculated within method of electron structure functions. The explicit expressions for the recoil proton polarization are represented as a contraction of the electron structure and the hard part of the polarization dependent contribution into cross-section. The calculation of the hard part with first order radiative correction is performed. The obtained representation includes the leading radiative corrections in all orders of perturbation theory and the main part of the second order next-to-leading ones. Numerical calculations illustrate our analytical results.Comment: 14 pages, 4 figure