Jordan-schwinger-type Realizations of Three-dimensional Polynomial Algebras
نویسنده
چکیده
A three-dimensional polynomial algebra of order m is defined by the commutation relations [P0, P±] = ±P±, [P+, P−] = φ (P0) where φ(P0) is an m-th order polynomial in P0 with the coefficients being constants or central elements of the algebra. It is shown that two given mutually commuting polynomial algebras of orders l and m can be combined to give two distinct (l + m + 1)-th order polynomial algebras. This procedure follows from a generalization of the well known Jordan-Schwinger method of construction of su(2) and su(1, 1) algebras from two mutually commuting boson algebras.
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