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.

考虑了高自旋规范场与标量场的局部四次相互作用。在这种特殊情况下，使用 Noether 程序的全部功能解决了为物理规范中的更高自旋场构建相互作用拉格朗日量的重要任务。结果，获得了线性现场规范变换，并分析了相应的变换换向器。为了理解这个代数的闭包，这个换向器的右侧根据来自三次相互作用的规范变换进行分类，这些变换来自不同的更高自旋对称张量场和混合对称张量场变换。