On manifolds admitting the consistent Lagrangian formulation for higher spin fields

摘要

We study a possibility of Lagrangian formulation for free higher spin bosonictotally symmetric tensor field on the background manifold characterizing by thearbitrary metric, vector and third rank tensor fields in framework of BRSTapproach. Assuming existence of massless and flat limits in the Lagrangian andusing the most general form of the operators of constraints we show that thealgebra generated by these operators will be closed only for constant curvaturespace with no nontrivial coupling to the third rank tensor and the strength ofthe vector fields. This result finally proves that the consistent Lagrangianformulation at the conditions under consideration is possible only in constantcurvature Riemann space.