Local quartic interaction of scalars with higher spin gauge fields and commutator of linear gauge transformations
April 23, 2021
Some special case of local quartic interaction of higher spin gauge field with a scalar field is considered. The nontrivial task of construction of interacting Lagrangian for the constrained higher spin field (physical gauge) was solved using the full power of Noether’s procedure. As a byproduct linear on-field gauge transformation is obtained and the corresponding closure of commutator of transformation is analyzed. The right-hand side of this commutator is classified in respect to gauge transformations coming from cubic interactions of a scalar with different higher spin symmetric tensor fields and with mixed symmetry tensor field transformations.
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