Improvement of the Blankenbecler-Sugar Approximation

Abstract

We present an approximate solution to the Bethe-Salpeter equation. It retains the attractive features of the Blankenbecler-Sugar approximation, while improving upon their results. For one-particle-exchange interactions, there is 110 increase in calculatio~lal difficulty with this technique.

50. Arabic Dialects (general article)

“…For him, this resulted, most particularly, in the loss of the case system and the erasure of mood differences in the verb. Ferguson (1959) 6the use of li-affixed to verbs for indirect objects 7the loss of polarity in the cardinal numbers 13Ϫ19 8the velarisation of /t/ in the cardinal numbers 13Ϫ19 9the disappearance of the feminine elative fuflā' Cohen (1970), who rejected the monogenetic explanation of the origin of the dialects, and Versteegh (1984), who controversially did not, propose a further twenty features. Versteegh's hypothesis is founded on a belief that the modern dialects are descended from one uniform linguistic entity Ϫ not Ferguson's military koine, as we saw above, but 'the essentially uniform language of the Jāhiliyya' Ϫ through a complex process of pidginisation, followed by creolisation and then de-creolisation (Versteegh 1984, 6).…”

Preliminaries on the Structural Aspects of A Spoken Variety: A case Study

“…Every variety has its peculiar characteristics which permit its assignment to a particular group. In order to distinguish between rural and urban varieties, only a restricted number of properly distinctive features, some phonetic and morphological, have been proposed by Cohen (1970). Rural varieties are characterised by the preservation of diphthongs which are realised as long vowels in urban varieties, [u:] for underlying /aw/ and [i:] for underlying /aj/.…”

Unitarity and the Bethe-Salpeter equation

“…In the Cohen [19] approximation it is assumed that the amplitude in Eq. ( 1) does not depend on the relative energy q ′′ 0 .…”

“…To examine the importance of the role of unitarity in the reduction of the BS equation, we examine a small class of three-dimensional equations that preserve some of the unitarity cuts in the BS equation. In particular, we consider the the Klein [17] or "equal-time" (ET) equation [6,18], the Cohen (C) approximation [19], the instantaneous (I) approximation [4,5,20,21] used recently by Pascalutsa and Tjon for πN scattering [21], and the Blankenbecler-Sugar (BbS) equation [22]. Since there are an infinite number of possible 3-D equations, there are many other equations that we could compare to the BS equation.…”

“…In particular, we consider the the Klein [17] or "equal-time" (ET) equation [6,18], the Cohen (C) approximation [19], the instantaneous (I) approximation [4,5,20,21] used recently by Pascalutsa and Tjon for πN scattering [21], and the Blankenbecler-Sugar (BbS) equation [22]. Since there are an infinite number of possible 3-D equations, there are many other equations that we could compare to the BS equation.…”