On-shell reduction of spin-zero Duffin-Kemmer-Petiau covariants and implications for the relativistic impulse approximation
Abstract
We analyze the on-shell content of the local Lorentz covariants of the five-dimensional spin-zero Duffin-Kemmer-Petiau algebra in elastic spin-zero-spin-1/2 scattering. The scalar, vector, and tensor structures are reduced explicitly to the two independent amplitudes allowed by the physical parity-conserving process. The two scalar structures are proportional on shell, the genuine nonminimal vector i[P,βμ] is longitudinal and vanishes after contraction with the conserved fermion vector current, and the projected vectors Pβμ and βμP each reduce to one half of the minimal-vector contribution. The tensor covariants introduce no additional on-shell directions. We discuss the consequences for the four invariant choices used in meson-nucleus optical-potential calculations and show that different nuclear equations can arise only after on-shell-equivalent representatives are promoted to optical operators and iterated beyond the order at which the elementary impulse approximation is fixed. These results provide a systematic basis for distinguishing genuinely independent elementary amplitudes from representation-dependent effects generated by the optical embedding.
Versions
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BibTeX
@misc{castro2026onshell,
title = {{On-shell reduction of spin-zero Duffin-Kemmer-Petiau covariants and implications for the relativistic impulse approximation}},
author = {Luis B. Castro},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37263},
eprint = {2610.37263},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37263},
}
RIS
TY - UNPB
TI - On-shell reduction of spin-zero Duffin-Kemmer-Petiau covariants and implications for the relativistic impulse approximation
AU - Luis B. Castro
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37263
UR - https://arxiv.org/abs/2610.37263
AB - We analyze the on-shell content of the local Lorentz covariants of the five-dimensional spin-zero Duffin-Kemmer-Petiau algebra in elastic spin-zero-spin-1/2 scattering. The scalar, vector, and tensor structures are reduced explicitly to the two independent amplitudes allowed by the physical parity-conserving process. The two scalar structures are proportional on shell, the genuine nonminimal vector i[P,β^μ] is longitudinal and vanishes after contraction with the conserved fermion vector current, and the projected vectors Pβ^μ and β^μP each reduce to one half of the minimal-vector contribution. The tensor covariants introduce no additional on-shell directions. We discuss the consequences for the four invariant choices used in meson-nucleus optical-potential calculations and show that different nuclear equations can arise only after on-shell-equivalent representatives are promoted to optical operators and iterated beyond the order at which the elementary impulse approximation is fixed. These results provide a systematic basis for distinguishing genuinely independent elementary amplitudes from representation-dependent effects generated by the optical embedding.
ER -