ABSTRACT
We track the origin of the subsidiary conditions satisfied by the RaritaSchwinger field as the set of equations constraining the field to the https://www.w3.org/1998/Math/MathML"> - 15 4 m 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq6922.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> eigensubspace of the squared Pauli-Lubanski vector in the https://www.w3.org/1998/Math/MathML"> 1 2 , 1 2 ⊗ 1 2 , 0 ⊕ 0 , 1 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq6923.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> irrep of the HLG. We explicitly formulate the corresponding second order equation, and show that the spin- 3/2 subspace with well defined parity can be pinned down by the one sole equation, https://www.w3.org/1998/Math/MathML"> i ε μαβσ γ 5 γ μ p σ - m g αβ ψ β = 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq6924.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . We gauge the latter equation and argue causal spin- 3/2 propagation within an electromagnetic field, thus resolving the Velo-Zwanziger problem.
