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From Lorentz to $SIM(2)$: contraction, four-dimensional algebraic relations and projective representations https://arxiv.org/abs/2504.13306 #mathph #mathMP #hepth

From Lorentz to $SIM(2)$: contraction, four-dimensional algebraic relations and projective representations

We present a comprehensive study on $SIM(2)$ and $ISIM(2)$ groups, their representations and algebraic aspects. 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.

arXiv.org
April 22, 2025 at 3:10 AM · · feed2toot · 0 · 0 · 0
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