Show that in 3D the translation operators (P_{j}) and rotation operators (L_{j}) given by Eq. (12.9) generate

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Show that in 3D the translation operators $P_{j}$ and rotation operators $L_{j}$ given by Eq. (12.9) generate the non-abelian Lie group $\mathrm{E}_{3}$, with the commutators (12.10).

Data from Eq. 12.9

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Data from Eq. 12.10

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Symmetry Broken Symmetry And Topology In Modern Physics A First Course

ISBN: 9781316518618

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Authors: Mike Guidry, Yang Sun

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Question Posted: Mar 30, 2024 11:00 PM

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Show that in 3D the translation operators (P_{j}) and rotation operators (L_{j}) given by Eq. (12.9) generate

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a Pj = -i- Lj = -i jkm xk Jxm

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Symmetry Broken Symmetry And Topology In Modern Physics A First Course

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