What question did this study set out to answer?

This research aims to investigate the algebraic structures and representations of symmetry groups in Very Special Relativity.

February 22, 2026

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

Key Points

This research aims to investigate the algebraic structures and representations of symmetry groups in Very Special Relativity.
Detailed examination of the Inönü-Wigner contraction method for group representations.
Application of Bargmann’s formalism to explore projective representations.
Analysis of local phase factors in relation to non-abelian groups.
Demonstrated a complete four-dimensional algebraic representation for the symmetry groups under consideration.
Identified the significance of phase factors in projective representations
Provided insights into the contraction of Lorentz groups and its implications for relativistic physics.

Abstract

We present a comprehensive study on Formula: see text and Formula: see text groups, their representations and algebraic aspects. These groups, together with Formula: see text, arise as the symmetry groups of Very Special Relativity (VSR), where full Lorentz invariance is reduced while retaining many relativistic consequences. After obtaining Formula: see text through the Inönü-Wigner contraction procedure, a complete four-dimensional algebraic representation is shown for Formula: see text and Formula: see text. 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.

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Cite This Study

Rodrigues et al. (Fri,) studied this question.

synapsesocial.com/papers/699a9d3c482488d673cd2f8d https://doi.org/https://doi.org/10.1142/s021988782650177x

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