We analyze the star -product induced on F(R^3) by a suitable reduction of the Moyal product defined on F(R^4). This is obtained through the identification R^3 with g∗, the dual of a three- dimensional Lie algebra. We consider the su(2) case, exhibit a matrix basis and realize the algebra of functions on su(2)∗ in such a basis. The relation to the Duflo map is discussed. As an application to quantum mechanics we compute the spectrum of the hydrogen atom.
ON THE ⋆-PRODUCT QUANTIZATION AND THE DUFLO MAP IN THREE DIMENSIONS / Rosa, Luigi; Vitale, Patrizia. - In: MODERN PHYSICS LETTERS A. - ISSN 0217-7323. - 27:(2012), pp. 1250207-1-1250207-15. [10.1142/S0217732312502070]
ON THE ⋆-PRODUCT QUANTIZATION AND THE DUFLO MAP IN THREE DIMENSIONS
ROSA, LUIGI;VITALE, PATRIZIA
2012
Abstract
We analyze the star -product induced on F(R^3) by a suitable reduction of the Moyal product defined on F(R^4). This is obtained through the identification R^3 with g∗, the dual of a three- dimensional Lie algebra. We consider the su(2) case, exhibit a matrix basis and realize the algebra of functions on su(2)∗ in such a basis. The relation to the Duflo map is discussed. As an application to quantum mechanics we compute the spectrum of the hydrogen atom.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
