Theory of one-dimensional relativistic elastic continuum for the model of particles and resonances

The theory of the relativistic string was originally formulated directly at quantum-mechanical level by the set of a wave equation and an infinite number of subsidiary conditions or equivalently by a super-wave equation. It is however, relevant to reconstruct the theory by first establishing the classical theory of a relativistic string explicitly and then quantizing it, because this makes the correspondence-theoretic foundation and realistic interpretation of the theory clearer, even though the final ingredients of the theory are the same as in the original one. Distinction is made between 'realistic viewpoint' and 'geometric viewpoint'. First the string theory is established in the realistic viewpoint, where each elementary constituent (say 'parton') of the string has three degrees of freedom. The most general and flexible representation of this theory is given in the 'partial general-covariant' form. Then by choosing a suitable gauge one obtains the 'Lorentz-covariant formalism'. Taking another gauge one gets the equivalent non-covariant formalism which directly exhibits the physical meaning of theory. Next the string theory is considered in the geometric viewpoint, The model obtained differs fron the realistic model because here each 'parton' has only two degrees of freedom and represents the case of vanishing intrinsic parton mass. It is shown that the string model implies a striking realization of 'realistic rotator model' by its states on the leading trajectory as well as by some other states. (Auth.)