Joss-Weinberg covariant field with mass and spin 3/2
Abstract
We present the explicit theory of the Joss-Weinberg covariant field with spin 3/2 which is a eight-dimensional massive covariant field transforming according to the representation (3/2,0)⊕(0, 3/2) of the group SL(2,ℂ). As the transformation matrices of this representation are still unknown, we apply a new method for deriving them using exclusively maximally reducible representations, e. g. (1,0)⊗(1/2,0) instead of the irreducible one (1,1/2)=(1,0)⊗(0,1/2) we meet in usual frameworks. After applying this method, we obtain a $12$-component covariant field transforming according to the representation [(1,0)⊗(1/2,0)]⊕ [(0,1)⊗(0, 1/2)] which is maximally reducible, up to subspaces of irreducible representations of the SU(2) group. Consequently, after developing the theory in the direct product basis of the representation (1,0)⊗(1/2,0), we can separate the sector of spin half revealing thus the genuine Joss-Weinberg covariant field of spin 3/2, transforming according to the representation (3/2,0)⊕(0, 3/2). In this manner the theory of Joss-Weinberg covariant field of spin 3/2 can be build naturally deriving the field equation and associated matrices, Lagrangian formalism, inner product and the closed expressions of the orthonormal mode spinors.
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BibTeX
@misc{cotaescu2026jossweinberg,
title = {{Joss-Weinberg covariant field with mass and spin $\frac32$}},
author = {Ion I. Cotaescu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.28877},
eprint = {2605.28877},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.28877},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Joss-Weinberg covariant field with mass and spin 3/2
AU - Ion I. Cotaescu
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2605.28877
UR - https://arxiv.org/abs/2605.28877
AB - We present the explicit theory of the Joss-Weinberg covariant field with spin 3/2 which is a eight-dimensional massive covariant field transforming according to the representation (3/2,0)⊕(0, 3/2) of the group SL(2,ℂ). As the transformation matrices of this representation are still unknown, we apply a new method for deriving them using exclusively maximally reducible representations, e. g. (1,0)⊗(1/2,0) instead of the irreducible one (1,1/2)=(1,0)⊗(0,1/2) we meet in usual frameworks. After applying this method, we obtain a $12$-component covariant field transforming according to the representation [(1,0)⊗(1/2,0)]⊕ [(0,1)⊗(0, 1/2)] which is maximally reducible, up to subspaces of irreducible representations of the SU(2) group. Consequently, after developing the theory in the direct product basis of the representation (1,0)⊗(1/2,0), we can separate the sector of spin half revealing thus the genuine Joss-Weinberg covariant field of spin 3/2, transforming according to the representation (3/2,0)⊕(0, 3/2). In this manner the theory of Joss-Weinberg covariant field of spin 3/2 can be build naturally deriving the field equation and associated matrices, Lagrangian formalism, inner product and the closed expressions of the orthonormal mode spinors.
ER -