19.4 For further reading

19.4 For further reading

Concept links · terms present in this machine draft; source roles are unverified: irreducible representation

The angular momentum operators are a standard topic in every quantum mechanics textbook, see for example chapter 12 of [81]. The characterization here of free particle wavefunctions at fixed energy as giving irreducible representations of the Euclidean group is not so conventional, but it is just a non-relativistic version of the conventional description of relativistic quantum particles in terms of representations of the Poincar´e group (see chapter 42). In the Poincar´e group case the analog of the $E(3)$ irreducible representations of non-zero energy $E$ and helicity n considered here will be irreducible representations labeled by a nonzero mass and an irreducible representation of $SO(3)$ (the spin). In the Poincar´e group case, for massless particles one will again see representations labeled by an integral helicity (an irreducible representation of $SO(2),$ , but there is no analog of such massless particles in the $E(3)$ case.

For more details about representations of $E(2)$ and $E(3)$ , see [95] or [98] (which is based on [93]).

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Appendix: conventions and notation

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原书 PDF · 印刷页 210、211、212、213、214、215、216、217、218、219、220

来源版本：2025-10-20

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