Singularities of Scattering Amplitudes on Unphysical Sheets and Their Interpretation

The analytic structure of two-particle scattering amplitudes on the unphysical sheet of the Riemann surface reached by crossing the two-particle cut is discussed. The singularities of the amplitudes there are shown to be poles and their physical interpretation is studied. The way in which bound states appear on the physical sheet in the Mandelstam representation, both as isolated poles and as cuts, is traced in detail. The properties of partial wave amplitudes and of the full amplitude as a function of energy and angle and of energy and momentum transfer are discussed. Finally, a few remarks are made in connection with unstable states

Three-body decays of the proton

The rates for the three-body proton decays p→ππe+ are related to the rate for the decay p→π0e+. This is done by making an ansatz for the form of the three-body amplitude which is consistent with current algebra and with the measured ππ final-state interactions. We find that the three-body decay rates are comparable with the rate for the two-body decay p→π0e+

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

Computations in Large N Matrix Mechanics

The algebraic formulation of Large N matrix mechanics recently developed by Halpern and Schwartz leads to a practical method of numerical computation for both action and Hamiltonian problems. The new technique posits a boundary condition on the planar connected parts X_w, namely that they should decrease rapidly with increasing order. This leads to algebraic/variational schemes of computation which show remarkably rapid convergence in numerical tests on some many- matrix models. The method allows the calculation of all moments of the ground state, in a sequence of approximations, and excited states can be determined as well. There are two unexpected findings: a large d expansion and a new selection rule for certain types of interaction.Comment: 27 page

Transverse Spectra of Radiation Processes in Medium

We develop a formalism for evaluation of the transverse momentum dependence of cross sections of the radiation processes in medium. The analysis is based on the light-cone path integral approach to the induced radiation. The results are applicable in both QED and QCD

Influence of the LPM effect and dielectric suppression on particle air showers

An analysis of the influence of the Landau-Migdal-Pomeranchuk (LPM) effect on the development of air showers initiated by astroparticles is presented. The theory of Migdal is studied and compared with other theoretical methods, particularly the Blankenbecler and Drell approach. By means of realistic computer simulations and using algorithms that emulate Migdal's theory, including also the so-called dielectric suppression, we study the behavior of the relevant observables in the case of ultra-high energy primaries. We find that the LPM effect can significantly modify the development of high energy electromagnetic showers in certain cases.Comment: 18 pages, 13 figures, 1 table. To appear in Phys. Rev.

The controversy in the γγ→ρρ\gamma\gamma\to\rho\rho process: potential scattering or qqqˉqˉqq\bar{q}\bar{q} resonance ?

The $\gamma\gamma\to\rho^0\rho^0\to 4 \pi$ reaction shows a broad peak at 1.5 GeV in the $(J^P,J_z)=(2^+,2)$ channel which has no counterpart in the $\rho^+\rho^-$ channel. This "resonance" is considered as a candidate for a $qq\bar q\bar q$ state in the "s-channel". We show, however, that it can also be explained by potential scattering of $\rho^0\rho^0$ via the $\sigma$- exchange in the "t-channel".Comment: 12 pages, latex, 3 postscript figures, to appear in Zeitschrift fur Physi