The Role of Boundary Conditions in Solving Finite-Energy, Two-Body, Bound-State Bethe-Salpeter Equations

The difficulties that typically prevent numerical solutions from being obtained to finite-energy, two-body, bound-state Bethe-Salpeter equations can often be overcome by expanding solutions in terms of basis functions that obey the boundary conditions. The method discussed here for solving the Bethe-Salpeter equation requires only that the equation can be Wick rotated and that the two angular variables associated with rotations in three-dimensional space can be separated, properties that are possessed by many Bethe-Salpeter equations including all two-body, bound-state Bethe-Salpeter equations in the ladder approximation. The efficacy of the method is demonstrated by calculating finite-energy solutions to the partially-separated Bethe-Salpeter equation describing the Wick-Cutkosky model when the constituents do not have equal masses.Comment: 18 page

Off-shell renormalization of the massive QED in the unitary gauge

Despite its simplicity, the unitary gauge is not a popular choice for practical loop calculations in gauge theories, due to the lack of off-shell renormalizability. We study the renormalization properties of the off-shell Green functions of the elementary electron fields in the massive QED, in order to elucidate the origin and structure of the extra ultraviolet divergences which exist only in the unitary gauge. We find that all these divergences affect the Green functions in a trivial way such that in coordinate space the off-shell Green functions are in fact multiplicatively renormalizable. This result may generalize to the abelian and non-abelian Higgs theories, for which the unitary gauge might bring much simplification to the loop calculations.Comment: LaTeX2e, 7 pages, no figure, minor revision in the introductory paragrap

The application of quantitative methods to the study of early development and ovarian structure in mammals

Introduction • I The Pluriovular Follicle, with Reference to its Occurrence in the Ferret • II The Technique of Estimating Small Irregular Areas in Biological Research, with Notes on the Tests of Accuracy • III The Early Development of the Ferret: the Pronuclei • IV The Measurement of Ferret Pronuclei • V The Sizes of Ferret Pronuclei • VI A Quantitative Study of the Polar Body of the Ferret, with a Note on the Second Polar Spindle • VII The Early Development of the Ferret: the Cytoplasm • VIII The Early Development of the Ferret: the Zona Granulosa, Zona Pellucida and Associated Structures • IX The Volumes of Ferret Ova, with Special Reference to the Methods of Determination • X A Study of the Sizes of Nuclei in Ovarian Stroma • Appendix -- Posterior Duplicity in a Dog, with • Reference to Mammalian Teratology in Genera

Political Instability in Developing Areas

Seen in broad sociological terms, the impact of economically and technologically advanced societies has disrupted every aspect of the developing world\u27s traditional societies and has touched off the complex processes of modernization and development