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Nanosystems: Phys. Chem. Math., 2022, 13 (3), 299–307

Ladder operators approach to representation classification problem for Jordan–Schwinger image of su(2) algebra

Gleb V. Tushavin – ITMO University, Saint Petersburg, Russia
Alexander I. Trifanov – ITMO University, Saint Petersburg, Russia
Ekaterina V. Zaitseva – ITMO University, Saint Petersburg, Russia

Corresponding author: Gleb V. Tushavin, gleb@tushavin.ru

DOI 10.17586/2220-8054-2022-13-3-299-307

ABSTRACT The eigenvalues of the complete commuting set of self-adjoint operators determine the classification of states. We construct a classification for the image of the Jordan–Schwinger mapping of the su(2) algebra. We use the ladder operator approach to construct a canonical basis of irreducible representations and define the self-adjoint operators of the complete commuting set.

KEYWORDS Ladder operators, su(2), Jordan–Schwinger map, representation theory

FOR CITATION Tushavin G.V., Zaitseva E.V., Trifanov A.I. Ladder operators approach to representation classification problem for Jordan–Schwinger image of su(2) algebra. Nanosystems: Phys. Chem. Math., 2022, 13 (3), 299–307.

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