Gauge invariant Lagrangian construction for massive bosonic higher spin fields in D dimensions

Abstract

We develop the BRST approach to Lagrangian formulation for massive higher integer spin fields on a flat space-time of arbitrary dimension. General procedure of gauge invariant Lagrangian construction describing the dynamics of massive bosonic field with any spin is given. No off-shell constraints on the fields (like tracelessness) and the gauge parameters are imposed. The procedure is based on construction of new representation for the closed algebra generated by the constraints defining an irreducible massive bosonic representation of the Poincare group. We also construct Lagrangian describing propagation of all massive bosonic fields simultaneously. As an example of the general procedure, we derive the Lagrangians for spin-1, spin-2 and spin-3 fields containing total set of auxiliary fields and gauge symmetries of free massive bosonic higher spin field theory.

Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space

“…Our purpose here is to construct the new enlarged operators satisfying some deformed algebra so that the new operators g 0 and l become zero or (as was shown in [31]) they contain arbitrary parameters which then defined from the condition that the supplementary equations do not give more restrictions on the basic vectors (6) in addition to (23). The method we apply in this paper for constructing the enlarged expressions for the operators is a generalization of the method used in our papers [30][31][32][33] where the operator algebras are Lie algebras.…”

“…Therefore if we are able to express the Lagrangian in terms of BRST charge, we automatically obtain the consistent gauge invariant Lagrangian formulation of the theory with all auxiliary fields. Namely such a situation is realized in free higher spin field models [23,[30][31][32][33] (see also the early application of BRST approach to interacting higher spin filed theory in [34]). …”

“…As it should be, the gauge invariance of massive theory means that the corresponding Lagrangian formulation includes the Stueckelberg fields. The approach under consideration is a generalization of works [30][31][32][33] on Lagrangian construction of higher spin fields in arbitrary dimensional Minkowski space. The BRST approach to higher spin fields in AdS space was first used in [23], where the bosonic massless fields were considered.…”

“…This occurs due to these operators are multiplied on the annihilation ghost operators in BRST operator (see relations (55) and (71), some details are discussed in [31]). …”

“…[30][31][32][33] for (20)- (22), (25), (26) the cases of higher spin fields in flat space). This happens because among the above hermitian operators there are operators which are not constraints (g 0 and l in the case under consideration) and they bring two more equations (in addition to (23)) on the physical field (6).…”