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

2025/04/17 by Rodrigues, J. E., Matzenbacher, J. M. B., da Rocha, G. M. Caires +1
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2504.13306

Abstract

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 \mathfraksim(2) and \mathfrakisim(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.

Citations

• Light-Light scattering in Very Special Relativity Quantum Electrodynamics and Cosmic Anisotropies
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• DISIMb(2) Local Relativistic Symmetry and Finslerian Extension of the Theory of Relativity
• Quantum field theory with a preferred direction: The very special relativity framework
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• Born-Infeld electrodynamics in very special relativity
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• Very Special Relativity and Lorentz Violating Theories
• Gauge theory and SIM(2) superspace
• VSR is incompatible with Thomas precession
• Sim(2) and SUSY
• Very Special Relativity
• A systematic construction of completely integrable Hamiltonians from coalgebras
• On Some Types of Topological Groups
• On Unitary Ray Representations of Continuous Groups

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