New Lie groups can be constructed from old by a process called group contraction. Contraction involves reparameterization of the Lie group’s parameter space in such a way that the group multiplication properties, or commutation relations in the Lie algebra, remain well defined even in a singular limit. In general, the properties of the original Lie group have well-defined limits in the contracted Lie group. For example, the parameter space for the contracted group is well defined and noncompact. Other properties with well-defined limits include: Casimir operators; basis states of representations; matrix elements of operators; and Baker–Campbell–Hausdorff formulas. Contraction provides limiting relations among the special functions ...

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