Local Casimir Energy For Solitons

Direct calculation of the one-loop contributions to the energy density of bosonic and supersymmetric phi-to-the-fourth kinks exhibits: (1) Local mode regularization. Requiring the mode density in the kink and the trivial sectors to be equal at each point in space yields the anomalous part of the energy density. (2) Phase space factorization. A striking position-momentum factorization for reflectionless potentials gives the non-anomalous energy density a simple relation to that for the bound state. For the supersymmetric kink, our expression for the energy density (both the anomalous and non-anomalous parts) agrees with the published central charge density, whose anomalous part we also compute directly by point-splitting regularization. Finally we show that, for a scalar field with arbitrary scalar background potential in one space dimension, point-splitting regularization implies local mode regularization of the Casimir energy density.Comment: 18 pages. Numerous new clarifications and additions, of which the most important may be the direct derivation of local mode regularization from point-splitting regularization for the bosonic kink in 1+1 dimension

On the origin of the West Indian Fauna

Many zoologists have attempted to solve this problem which is a complicated one. In one respect the views of almost all agree. It is in the belief that the West Indian islands must have undergone profound alterations in configuration during the past. It is thought that at one time they must all have formed a continuous land surface. At another time, as has been suggested, some of them were attached to a neighbouring mainland of which they formed large promontories. At still another period of their history some at any rate of the islands must have been smaller than they are now. Many botanists and geologists agree with these theories, and these views imply that the animals and plants now living on the Antilles have mainly wandered to the islands from the Continent at a time when the latter were connected with one another. One of the strongest arguments in favour of the former land connection of an island with the neighbouring Continent is the occurrence on the island of such mammals as could not have been transported there by human agency. As regards the Antilles, objections have been raised to this argument on account of the paucity of the mammalian fauna on the islands as compared with the wealth of the mammals on the mainland. Within recent years however, these islands have yielded quite a number of fossil types of mammals thus greatly strengthening the opinion that the West Indies owe their fauna to the fact of their having once been joined to the mainland. Nevertheless as some authorities still maintain that the Antilles have never been connected by land with the adjoining Continents — at any rate not in Tertiary times — it may be of interest once more to review this most important aspect of the Antillean problem