Abstract
Local quartic interaction of higher-spin gauge field with a scalar field is considered. In this special case, the nontrivial task of construction of interacting Lagrangian for the higher spin field in physical gauge was solved using the full power of Noether's procedure. As a result, the linear on-field gauge transformation is obtained and the corresponding commutator of transformation is analyzed. To understand the closure of this algebra the right-hand side of this commutator is classified in respect to gauge transformations coming from cubic interactions with different higher spin symmetric tensor fields and with mixed symmetry tensor fields transformations.
Highlights
The problem of construction of complete Higher Spin (HS) Interaction Lagrangian is one of the tasks with smoldering interest for last forty years [1]-[7]
To understand the closure of this algebra the right-hand side of this commutator is classified in respect to gauge transformations coming from cubic interactions with different higher spin symmetric tensor fields and with mixed symmetry tensor fields transformations
We considered the possibility to construct local quartic interaction in the special case of two higher spin gauge fields and two scalars
Summary
The problem of construction of complete Higher Spin (HS) Interaction Lagrangian is one of the tasks with smoldering interest for last forty years [1]-[7]. It seems that in some special cases it is possible to construct some local interactions between fields with different spins at least as a part of a more complicated covering theory (maybe non-local) including other gauge fields and symmetries. We construct some special local quartic interaction of two scalars and two spin four fields using standard Noether’s procedure. Second important point that we constructing quartic vertex we derive fixed linear in gauge field gauge transformation of our HS field δ1(ǫ) and be able to investigate the closure of commutators of two such a transformation [δ1(η)δ1(ǫ)] ∼ δ1([η,ǫ]) + additional terms and understand whether it leads to nonlocality or not. The calculations which we have performed here are based on the technique and notation developed in the past in [46]-[49]
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