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

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

1995-03-09

arxiv.org/abs/q-alg/9503004v1

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 17 pages

Scientific paper

10.1007/BF00714403

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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