One of the possible approaches to the construction of massive higher spin interactions is to use their gauge invariant description based on the introduction of the appropriate set of Stueckelberg fields. Recently, the general properties of such approach were investigated by Boulanger etal (2018 J. High Energy Phys. JHEP07(2018)021). The main findings of this work can be formulated in two statements. At first, there always exist enough field redefinitions to bring the vertex into abelian form where there are some corrections to the gauge transformations but the gauge algebra is undeformed. At second, with the further (as a rule higher derivative) field redefinitions one can bring the vertex into trivially gauge invariant form expressed in terms of the gauge invariant objects of the free theory. Our aim in this work is to show (using a simple example) how these general properties are realised in the so-called Fradkin–Vasiliev formalism and to see the effects (if any) that the presence of massless field, and hence of some unbroken gauge symmetries, can produce. As such example we take the gravitational interaction for massive spin-³/₂ field so we complete the investigation started by Buchbinder etal (2014 Eur. Phys. J. C 74 3153) relaxing all restrictions on the number of derivatives and allowed field redefinitions. We show that in spite of the presence of massless spin-2 field, the first statement is still valid, while there exist two abelian vertices which are not equivalent on-shell to the trivially gauge invariant ones. Moreover, it is one of this abelian vertices that reproduce the minimal interaction for massive spin-³/₂.

构建大规模高自旋相互作用的一种可能方法是使用他们基于引入适当的 Stueckelberg 场集的规范不变描述。最近，Boulanger等人(2018 J. High Energy Phys.JHEP07(2018)021)。这项工作的主要发现可以用两个陈述来表述。起初，总是存在足够的域重新定义来将顶点转化为阿贝尔形式，其中规范变换有一些修正，但规范代数未变形。其次，通过进一步的（通常是更高导数的）场重新定义，人们可以将顶点带入以自由理论的规范不变对象表示的平凡规范不变形式。我们在这项工作中的目的是展示（使用一个简单的例子）这些一般性质是如何在所谓的弗拉德金-瓦西里耶夫形式主义中实现的，并看到无质量场的存在的影响（如果有的话），因此一些不间断的规范对称性，可以产生。作为这样的例子，我们采用大规模自旋的引力相互作用 - ³/ ₂字段，因此我们完成了 Buchbinder等人(2014 Eur. Phys. J. C 74 3153)开始的调查，放宽了对导数数量的所有限制并允许重新定义字段。我们表明，尽管存在无质量自旋 2 场，但第一个陈述仍然有效，同时存在两个阿贝尔顶点，它们在壳上不等同于平凡规范不变的顶点。此外，正是这个阿贝尔顶点之一再现了大规模自旋³ / ₂的最小相互作用。