Читать книгу Quantum Mechanics for Nuclear Structure, Volume 2 - Professor Kris Heyde - Страница 28

1 Starting from the state ∣j,−j〉, the raising action of Γ(J+) terminates at n=2j (as it should for SU(2)).

2 The representation is non-unitary, i.e. Γ(J+)†≠Γ(J−) for scalar products defined on Bargmann measure (for which (∂∂z)†=z).

3 This type of non-unitary representation is an example of a Dyson representation [5].

4 The ∣z〉II basis is defined on an SU(2) irrep labelled by j, i.e. it is a linear combination of the states ∣jm〉, m=j,j−1,…,−j.