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We formulate the conditions defining the irreducible continuous spinrepresentation of the four-dimensional Poincar\'e group based on spin-tensorfields with dotted and undotted indices. Such a formulation simplifies analysisof the Bargmann-Wigner equations and reduces the number of equations from fourto three. Using this formulation we develop the BRST approach and derive thecovariant Lagrangian for the continuous spin fields.

BRST approach to Lagrangian construction for bosonic continuous spin field