Abstract
The standard group theoretic construction of coherent states has recently been extended to simple Lie supergroups, yielding the so-called supercoherent states. Usual coherent states for semi-simple Lie groups are parameterized by points of a symplectic homogeneous space, which is moreover a Kähler manifold. Analogously, we show here that the OSp(1/2) coherent states are parameterized by an OSp(1/2) supersymplectic homogeneous superspace. This turns out to be a non-trivial example of Rothstein’s general supersymplectic supermanifolds, and leads to the definition of the notion of a super Kähler supermanifold. This new subcategory of supermanifolds is well suited for the super extension of geometric quantization. Indeed, super Kähler supermanifolds are naturally equipped with a super Kähler polarization. The full geometric quantization procedure is here extended to the super Kähler homogeneous superspace underlying the OSp(1/2) coherent states. The present talk is based on results obtained in Refs. 1 and 2.
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El Gradechi, A.M. (1994). Supercoherent States and Geometric Quantization of a Super Kähler Supermanifold. In: Antoine, JP., Ali, S.T., Lisiecki, W., Mladenov, I.M., Odzijewicz, A. (eds) Quantization and Infinite-Dimensional Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2564-6_8
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DOI: https://doi.org/10.1007/978-1-4615-2564-6_8
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