On the $\star$-product quantization and the Duflo map in three dimensions

Abstract

We analyze the star product induced on the algebra of functions on R^3 by a suitable reduction of the Moyal product defined on F(R^4). This is obtained through the identification of R^3 with 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 its dual 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.

Misprints corrected. Journal ref. added

References in corpus (6)

• Group field theory with non-commutative metric variables
• Star products, duality and double Lie algebras
• Three Dimensional Quantum Geometry and Deformed Poincare Symmetry
• Twisted Noncommutative Field Theory with the Wick-Voros and Moyal Products
• Duality symmetry for star products
• A unifying perspective on the Moyal and Voros products and their physical meanings

Cited by in corpus (1)

• Noncommutative field theories on $R_{\lambda }^3$: Towards UV/IR mixing freedom