Nuclear Physics BI00 (1975) 157-178 © North-Holland Publishing Company CLASSICAL SOLUTIONS FOR THE RELATIVISTIC THREE-STRING BARYON PROBLEM P.A. COLLINS University o f Lancaster J.F.L. HOPKINSON Daresbury Laboratory R.W. TUCKER University o f Lancaster and Daresbury Laboratory Received 23 July 1975 The dynamical system consisting of three relativistic massless strings, self coupled at a common junction, is investigated classically. The equations of motion are generated from the fundamental action used to describe the single string. An essentially non-linear free boundary problem is recognised in the orthogonal transverse gauge and a large class of solutions is obtained. The leading Regge slopes associated with some of these solutions are calculated and their implications for a viable model of a baryon discussed. 1. Introduction The description of mesons in terms of the open relativistic string has reached a high degree of mathematical sophistication. The concepts of string fusion and fis- sion lead to an elegant, although mathematically complex, interpretation of the conventional dual model. The theory has been extended to incorporate closed and intrinsically spinning strings [ 1]. In this way the pomeron and Neveu-Schwarz sec- tors of the operator formalism have been satisfactorily re-interpreted. In a previous paper [2] we have formulated a second quantised functional field theory of hadron strings. We stressed therein its general applicability to topologies other than that of the open string. The approach was based on Feynman's principle [3] for quantising a dynamical system possessing a classical action. To establish the function space needed in such theories we are required to solve the system classically. Apart from quantum fluctuations the classical action contains much of the information needed for the quantum description of the system. In this paper we attempt to solve for the classical motion of a string system con- taining a bifurcation junction in space. The current dual model of a fermion [1] has 157