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Phase Space Reduction for Star-Products: An Explicit Construction for CP^n

M. Bordemann·M. Brischle·C. Emmrich·S. Waldmann
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Abstract

We derive a closed formula for a star-product on complex projective space and on the domain $SU(n+1)/S(U(1)\times U(n))$ using a completely elementary construction: Starting from the standard star-product of Wick type on $C^{n+1} \setminus \{ 0 \}$ and performing a quantum analogue of Marsden-Weinstein reduction, we can give an easy algebraic description of this star-product. Moreover, going over to a modified star-product on $C^{n+1} \setminus \{ 0 \}$, obtained by an equivalence transformation, this description can be even further simplified, allowing the explicit computation of a closed formula for the star-product on $\CP^n$ which can easily transferred to the domain $SU(n+1)/S(U(1)\times U(n))$.

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BibTeXRIS

M. Bordemann, M. Brischle, C. Emmrich, S. Waldmann. 1995-03-09. Phase Space Reduction for Star-Products: An Explicit Construction for CP^n. https://doi.org/10.1007/bf00714403

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