On manifolds admitting the consistent Lagrangian formulation for higher spin fields

Abstract

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

11 pages; v2: minor typos corrected, a reference added

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• General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. I. Bosonic fields
• General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. 2. Fermionic fields
• Higher-Spin Modes in a Domain-Wall Universe
• Quartic interaction vertex in the massive integer higher spin field theory in a constant electromagnetic field
• Lagrangian formulation of massive fermionic higher spin fields on a constant electromagnetic background
• The Involutive System of Higher-Spin Equations
• General Backgrounds for higher spin massive particles
• Equation for one-loop divergences in two dimensions and its application to higher spin fields