Regge Poles in High-Energy Electron Scattering

The possibility that the photon is described by a Regge trajectory is considered, and the effect of this assumption on the analysis of electron-pion, electron-nucleon, and electron-helium scattering is examined in some detail. Partial-wave projections for the various amplitudes are made in the annihilation channel, and a multiparticle unitarity condition is formally imposed by use of the N/D matrix formulation. Since the photon does not have a fixed spin of one, the spin matrix structure is considerably more complicated than in the conventional theory. The amplitudes are written in terms of the Regge poles corresponding to the photon, ρ-ω meson, etc., and the resulting cross sections are given in the interesting high-energy limit. In contrast to the usual analysis, where form factors depend only on the momentum transfer, we find a larger number of independent functions which depend on the energy as well, however, in a characteristic manner. That is, the essential change due to the Regge behavior of the photon is an over-all nonintegral power of the energy occurring in the cross section. The effect of this factor can be experimentally tested and this possibility is discussed

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

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

Bound-State Model of Weak and Strong Interactions

The pion-nucleon coupling constant is calculated from first principles by use of the N/D matrix method. Three models are introduced which contain pions, nucleons, and weakly interacting intermediate bosons of the scalar, pseudoscalar, and vector variety. The basic interactions are taken to be parity and isotopic spin conserving. Certain physical assumptions in the nature of boundary conditions and the known fact that the weak coupling is very weak, together with use of the Born approximation for N, enable us to obtain an eigenvalue equation which expresses the pion-nucleon coupling constant in terms of the three masses in the problem. The correct value for gπ^2 can be obtained for an intermediate vector meson of mass comparable to the nucleon mass with essentially no cutoff employed; on the other hand, the experimental value is also obtained with a spin-zero boson and a relatively small cutoff energy

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+

A Maximum Entropy Method of Obtaining Thermodynamic Properties from Quantum Monte Carlo Simulations

We describe a novel method to obtain thermodynamic properties of quantum systems using Baysian Inference -- Maximum Entropy techniques. The method is applicable to energy values sampled at a discrete set of temperatures from Quantum Monte Carlo Simulations. The internal energy and the specific heat of the system are easily obtained as are errorbars on these quantities. The entropy and the free energy are also obtainable. No assumptions as to the specific functional form of the energy are made. The use of a priori information, such as a sum rule on the entropy, is built into the method. As a non-trivial example of the method, we obtain the specific heat of the three-dimensional Periodic Anderson Model.Comment: 8 pages, 3 figure

Hole Pockets in the Doped 2D Hubbard Model

The electronic momentum distribution ${\rm n({\bf k})}$ of the two dimensional Hubbard model is studied for different values of the coupling ${\rm U/t}$, electronic density ${\rm \langle n \rangle}$, and temperature, using quantum Monte Carlo techniques. A detailed analysis of the data on $8\times 8$ clusters shows that features consistent with hole pockets at momenta ${\rm {\bf k}=(\pm {\pi\over{2}},\pm {\pi\over{2}})}$ appear as the system is doped away from half-filling. Our results are consistent with recent experimental data for the cuprates discussed by Aebi et al. (Phys. Rev. Lett. {\bf 72}, 2757 (1994)). In the range of couplings studied, the depth of the pockets is maximum at ${\rm \langle n \rangle \approx 0.9}$, and it increases with decreasing temperature. The apparent absence of hole pockets in previous numerical studies of this model is explained.Comment: 11 pages, 4 postscript figures appended, RevTeX (version 3.0

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.

Abelian Landau-Pomeranchuk-Migdal effects

It is shown that the high-energy expansion of the scattering amplitude calculated from Feynman diagrams factorizes in such a way that it can be reduced to the eikonalized form up to the terms of inverse power in energy in accordance with results obtained by solving the Klein-Gordon equation. Therefore the two approaches when applied to the suppression of the emission of soft photons by fast charged particles in dense matter should give rise to the same results. A particular limit of thin targets is briefly discussed.Comment: 14 pages, LATEX, 1 Fig. ps, submitted to Mod. Phys. Lett.