A Coding of Real Null Four-Momenta into World-Sheet Coordinates

The results of minimizing the action for string-like systems on a simply-connected world sheet are shown to encode the Cartesian components of real null momentum four-vectors into co-ordinates on the world sheet. This identification arises consistently from different approaches to the problem. 1 Recapitulation This article is based upon an old unpublished article with David Roberts, [1] which dates back to circa 1972, on a model for amplitudes suggested by string theory, or rather the dual resonance model as it was then called. (The results in this paper are recorded in the PhD thesis of Roberts [2]). I was so overwhelmed by the evident truth of the famous paper of Goddard, Goldstone Rebbi and Thorn quantising the bosonic string in 26 dimensions [6], which I regard as one of the classic papers in string theory, that I never submitted this article for publication, and after some consideration, decided not to seek publication for this version, rewritten in January of this year. However since recently there has appeared an article by Sommerfield and Thorn [3], the 4th section of which is closely related to the model presented in [1], it may be an appropriate time to give these ideas an airing. Also other recent developments have given rise to an interpretation of maximally violating helicity (MHV) amplitudes in Yang Mills theory in terms of topological string amplitudes [4], the connection between null-four vectors and Koba-Nielsen variables which is at the heart of [1] may not be entirely coincidental. The intention was to