Quantum dynamics of a massless relativistic string

Abstract

Abstract We develop the classical and quantum mechanics of a massless relativistic string, the light string, which is characterized by an action proportional to the area of the world sheet swept out by the string in space time. We show that, classically, there are only D -2 dynamically independent components among the D functions x μ ( σ , τ ) which represent the world sheet ( D is the dimension of space time). Quantizing only these independent components, we find that the angular momentum operators suggested by the correspondence principle generate O( D -1,1) only when the first excited state is a photon, i.e., a spin-one massless state, and when D = 26. By allowing additional degrees of freedom in the quantum mechanics, we are able to quantize the string in a Lorentz covariant manner for any value of D and any mass for the first excited state. In this latter scheme the full Fock space contains negative norm states. However, when D ⩽ 26 for a massless first excited state and D ⩽ 25 for a real massive first excited state, the physical states span a positive subspace of the Fock space. The excitation spectrum of the light string coincides with the space of physical states in the dual resonance model for unit intercept of the leading Regge trajectory. We point out the connection of this work to previous studies of the physical states in dual models.