Relativistic strings and dual models of the strong interactions

A review is given of the theory of strong interactions based on the model in which hadrons are represented as one-dimensional elastic relativistic systems (“strings”). The relation between this model and the concepts of quarks and partons is discussed. Basic results pertaining to Veneziano's dual theory, which can be regarded as a consequence of the string model, and modifications of this theory are considered. A detailed account of the classical theory of strings is given. The main emphasis is on those problems which are important in constructing a quantum theory, namely Hamiltonian mechanics and conformal symmetry. The quantization procedure is described and is shown to be self-consistent only in a 26-dimensional space with a special condition on the spectrum of states. A theory of strings with distributed spin is considered. Spin is introduced by means of the formalism of Grassman algebras. Quantization is then possible only in a 10-dimensional space. Interactions of strings take place by virtue of their rupture and recombination. A method of calculating interaction amplitudes is given. Discussions of the Koba-Nielsen representation, the continuum integral, and the two-dimensional conformal group are included in an appendix.