Quantization of a String of Spinning Material—Hamiltonian and Lagrangian Formulations

The dynamics of a relativistic string made of spinning material is discussed in two different formulations. The first is a manifestly covariant formulation under a gauge transformation. The second is a Hamiltonian formalism which enables us to make the transition from the classical to the quantum description in a coherent way. The Lagrangian is also constructed. The results of our investigations are as follows: (1) The mass spectra here coincide with those of the Neveu-Schwarz model. (2) The model is ghost-free. (3) The Poincaré generators ${\mathfrak{M}}^{\mu \nu }$ and ${\mathfrak{P}}^{\mu }$ are constructed. The quantization is shown to be consistent with Lorentz covariance if the dimension of space-time is 10 and the Regge intercept is ½.