Theory of Relativistic String and Super-Wave Equation. I

Abstract

In this and succeeding papers we reconstruct the theory of relativistic string, taken as a model of hadrons, in a general and unifying framework. In this paper the classical foundation of the “realistic” string theory is clarified. The theory is derived from the action integral which is invariant under “partial general transformation” on the parameters (σ, τ) for the world sheet traced by a motion of the string, and the fundamental equations are originally covariant under this group. Then by choosing a suitable gauge we obtain Lorentz-covariant formalism associated with constraints. We analyze is characteristics and obtain solutions. Taking another gauge we get the equivalent “Lorentz non-covariant formalism” free from constraint. This directly exhibits the physical meaning of the theory and also leads to its standard Hamiltonian formalism. Several conservation laws characteristic to our string theory are given.