Generators of the Poincaré Group for arbitrary tensors and spinor-tensors
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914826238820352 |
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| author | Silva, H. V. Almeida Dalmazi, D. Santos, R. R. Lino dos Mendonça, E. L. |
| author_facet | Silva, H. V. Almeida Dalmazi, D. Santos, R. R. Lino dos Mendonça, E. L. |
| contents | In this work, we systematically derive explicit expressions for the Poincaré Group generators on arbitrary-rank tensors and spinor-tensors in $D=3+1$ and $D=2+1$ spacetimes, thus generalizing previous works in the literature for the groups $ISO(3,1)$ and $ISO(2,1)$. From the Casimir eigenvalue equations, we demonstrate in a model-independent way the Fierz-Pauli constraints for massive particles for spins $\mathfrak{s}=5/2$, 3, and 4 in $D=3+1$ and helicities $α=5/2$, 3, and 4 in $D=2+1$ dimensions. We also comment on the demonstration of the Fierz-Pauli constraints for the general case of arbitrary spin (helicity). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_05728 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generators of the Poincaré Group for arbitrary tensors and spinor-tensors Silva, H. V. Almeida Dalmazi, D. Santos, R. R. Lino dos Mendonça, E. L. High Energy Physics - Theory In this work, we systematically derive explicit expressions for the Poincaré Group generators on arbitrary-rank tensors and spinor-tensors in $D=3+1$ and $D=2+1$ spacetimes, thus generalizing previous works in the literature for the groups $ISO(3,1)$ and $ISO(2,1)$. From the Casimir eigenvalue equations, we demonstrate in a model-independent way the Fierz-Pauli constraints for massive particles for spins $\mathfrak{s}=5/2$, 3, and 4 in $D=3+1$ and helicities $α=5/2$, 3, and 4 in $D=2+1$ dimensions. We also comment on the demonstration of the Fierz-Pauli constraints for the general case of arbitrary spin (helicity). |
| title | Generators of the Poincaré Group for arbitrary tensors and spinor-tensors |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.05728 |