On equivalence of gauge-invariant models for massive integer-spin fields
There are several approaches to formulate gauge-invariant models for massive integer-spin fields in $d$ dimensions including the following: (i) in terms of symmetric tensor fields $ϕ_{μ_1 \dots μ_k} $, with $k = s, s-1, \dots , 0$, restricted to be double traceless for $k\geq 4$; and (ii) in terms of a quartet of $traceful$ symmetric tensor fields $ψ_{μ_1 \dots μ_k} $, of rank $k=s,s-1,s-2, s-3$. We demonstrate that these formulations in Minkowski space ${\mathbb M}^d$ are equivalent to the gauge-invariant theory for a massive integer-spin field proposed in 1989 by Pashnev. We also make use of the Klishevich-Zinoviev theory in ${\mathbb M}^d$ to derive a unique generalisation of the Singh-Hagen model for a massive integer-spin field in $d>4 $ dimensions.