Exceptional Waves and Characteristic Shocks on Non-Linear Relativistic Strings

Abstract

Euler-Lagrange equations of a relativistic massive string are analysed from the stand­ point of non-linear wave propagation theory. Complete exceptionality is shown to hold, while strict exceptionality (usual in non-linear physical theories) appears only for non­ vanishing value of the masses at the ends, when time-like or light-like gauge specification is employed. § 1. Physical characters and applications of string-like models The study of relativistic stringv played quite a significant role in the recent development of hadrodynamics and strong field theory. The capability of Nambu string model) of reproducing the main results of high energy strong interaction phenomenology as: a) Regge behaviour and linearly rising Regge trajectories 3) b) The structure of dual resonance models (DRM) 4) c) A Hagedorn-like state density distribution 5) suggested the idea that the hadrons could be thought like extended structures and in particular one space dimensional. In fact some attempts of generalizing the string model to an N-dimensional system showed that for N> 1 either the linearity of Regge trajectories 6) or the Hagedorn-like distribution is lost.n In the following years the programme of finding a string theory for every known dual model has been carried out. It has been shown that the open string predicts the usual Veneziano amplitude, while the closed string is related to the Shapiro-Virasoro model 8) and the pomeron. The introduction of spin degrees of freedom (Iwasaki and Kikkawa) o) allowed obtaining the super gauge conditions appearing in the mod­ els of Ramond 101 and Neveu-Schwarz.ll) All the previous systems are ghost-free, but exhibit tachyons in the mass spectrum and predict an unphysical dimensionality of space-time (D>4). Recently some results have been obtained in the direction of more physical models.l2) From the point of view of usual field theory the appearance of extended n The author is a member of the G.N.F.M. of the C.N.R. ttl Also Istituto Nazionale di Fisica Nucleare, Sez. di Bologna.