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The focus of this chapter is the construction of a family of representations \({\hat{\hat{U}}}_{a}\) , \(a \geqslant 0\) , of the Poincaré group in 3 steps. For every \(a \geqslant 0\) , in the first step, we construct a strongly continuous unitary representation of the restricted Lorentz group, the connected component of the Lorentz group that contains the unit element, and analyze the generators of one-parameter subgroups associated with rotations and Lorentz boosts.

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A Family of Representations of the Poincaré Group

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  • 发表日期：

    2026年

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  • Reinhard Horst Beyer

摘要

The focus of this chapter is the construction of a family of representations \({\hat{\hat{U}}}_{a}\) , \(a \geqslant 0\) , of the Poincaré group in 3 steps. For every \(a \geqslant 0\) , in the first step, we construct a strongly continuous unitary representation of the restricted Lorentz group, the connected component of the Lorentz group that contains the unit element, and analyze the generators of one-parameter subgroups associated with rotations and Lorentz boosts.