From Lorentz to $SIM(2)$: contraction, four-dimensional algebraic relations and projective representations
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915870296506368 |
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| author | Rodrigues, J. E. Matzenbacher, J. M. B. da Rocha, G. M. Caires da Silva, J. M. Hoff |
| author_facet | Rodrigues, J. E. Matzenbacher, J. M. B. da Rocha, G. M. Caires da Silva, J. M. Hoff |
| contents | We present a comprehensive study on $SIM(2)$ and $ISIM(2)$ groups, their representations and algebraic aspects. These groups, together with $HOM(2)$, arise as the symmetry groups of Very Special Relativity (VSR), where full Lorentz invariance is reduced while retaining many relativistic consequences. After obtaining $SIM(2)$ through the Inönü-Wigner contraction procedure, a complete four-dimensional algebraic representation is shown for $\mathfrak{sim(2)}$ and $\mathfrak{isim(2)}$. Besides that, we apply Bargmann's formalism to investigate the (projective) representations for both cases, keeping track of the source of phase factors. We complete the study by presenting a particularly simple analysis to probe the existence of local phase factors, which is useful when dealing with non-abelian groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_13306 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Lorentz to $SIM(2)$: contraction, four-dimensional algebraic relations and projective representations Rodrigues, J. E. Matzenbacher, J. M. B. da Rocha, G. M. Caires da Silva, J. M. Hoff Mathematical Physics High Energy Physics - Theory We present a comprehensive study on $SIM(2)$ and $ISIM(2)$ groups, their representations and algebraic aspects. These groups, together with $HOM(2)$, arise as the symmetry groups of Very Special Relativity (VSR), where full Lorentz invariance is reduced while retaining many relativistic consequences. After obtaining $SIM(2)$ through the Inönü-Wigner contraction procedure, a complete four-dimensional algebraic representation is shown for $\mathfrak{sim(2)}$ and $\mathfrak{isim(2)}$. Besides that, we apply Bargmann's formalism to investigate the (projective) representations for both cases, keeping track of the source of phase factors. We complete the study by presenting a particularly simple analysis to probe the existence of local phase factors, which is useful when dealing with non-abelian groups. |
| title | From Lorentz to $SIM(2)$: contraction, four-dimensional algebraic relations and projective representations |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2504.13306 |