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 𝜙𝜇1…𝜇𝑘, with 𝑘 =𝑠,𝑠 −1,…,0, restricted to be double traceless for 𝑘 ≥4; and (ii) in terms of a quartet of traceful symmetric tensor fields 𝜓𝜇1…𝜇𝑘, of rank 𝑘 =𝑠,𝑠 −1,𝑠 −2,𝑠 −3. We demonstrate that these formulations in Minkowski space 𝕄𝑑 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 𝕄𝑑 to derive a unique generalization of the Singh-Hagen model for a massive integer-spin field in 𝑑 >4 dimensions.