Quantum Lorentz covariance in the light-cone string field theory

Abstract

The Lorentz covariance of the light-cone string field theory of the bosonic orientable open-closed mixed system in 26 dimensions is studied. The Lorentz algebra defined by the classical Poisson bracket does not close. The quantum commutators of the Lorentz generators and the hamiltonian are defined by using the Bjorken-Johnson-Low limit and are computed in the perturbation theory. It is shown that the algebra closes at the quantum level to all orders of the perturbation theory up to possible effects of divergences in loop amplitudes. The non-vanishing terms at the tree level, which violate the covariance, are cancelled by anomalies of the open string one-loop terms and there is no higher-loop anomaly.