R. J. Eden

Acnodes and Cusps on Landau Curves

It is shown that the Landau curve for a reduced sixth‐order diagram can acquire acnodes and real cusps as the masses are varied. They are associated with complex singularities that under certain conditions are in the physical sheet and cause a breakdown of the Mandelstam representation. The problem of obtaining general criteria for acnodes and cusps is discussed.

REGGE POLES AND BRANCH CUTS FOR POTENTIAL SCATTERING

The analytic properties of partial wave amplitudes are studied for complex energy and angular momentum. The properties of the wavefunctions are first obtained by standard methods in the theory of differential equations for general classes of potentials, and the effects of the dominant singular term in the potential near the origin are investigated. These include the appearance of branch cuts in the angular‐momentum variable for potentials which are singular like z−2, and the location of Regge poles for more singular potentials. The trajectories of Regge poles are also studied with particular reference to their behavior in the angular‐momentum plane as the energy tends to infinity. An example is given of a singular potential in which the trajectories move to infinity in a complex direction, contrary to the normal behavior for which they tend to negative integers. The real sections of Regge surfaces are also briefly discussed.

Regge poles and elementary particles

This is a review of Regge theory that is intended both as an introduction to its main features and as a survey of its relation to experimental results on the strong interactions of elementary particles. It includes a survey of the experimental and theoretical background that is required for an understanding of Regge theory. The central part of the review describes the basic ideas of Regge theory and the application of Regge pole models to high-energy collisions of elementary particles. The review concludes with a brief account of extensions of Regge theory that give the Veneziano representation and that give some features of many-particle production in high-energy collisions.

World energy to 2050: Outline scenarios for energy and electricity

Abstract This paper explores two outline scenarios for the year 2050. The one with a lower environmental impact involves a targeted efficiency future in which per capita energy use in the industrialized countries is halved by the year 2050, while in the developing countries it is doubled. The most important driving forces for future growth in demand in the developing countries are their increasing population and their need for more services requiring the use of energy and electricity. Less than doubling in per capita energy would imply unacceptable levels of growth in these services. In the targeted efficiency future world total commercial energy demand increases by more than 50%; the share arising from the developing countries increases from its present value of one-quarter of the total to nearly three-quarters of the total in the year 2050, and total carbon emissions increase. World electricity demand continues to increase, but the rate of growth becomes much lower than in the past, in response to improved efficiencies and saturation of demand in the industrialized countries, and to improved efficiencies and shortage of investment capital in the developing countries.