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arXiv · 1709.08531

A unitary "quantization commutes with reduction" map for the adjoint action of a compact Lie group

Brian C. Hall·Benjamin D. Lewis
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Abstract

Let $K$ be a simply connected compact Lie group and $T^{\ast}(K)$ its cotangent bundle. We consider the problem of "quantization commutes with reduction" for the adjoint action of $K$ on $T^{\ast}(K).$ We quantize both $T^{\ast}(K)$ and the reduced phase space using geometric quantization with half-forms. We then construct a geometrically natural map from the space of invariant elements in the quantization of $T^{\ast}(K)$ to the quantization of the reduced phase space. We show that this map is a constant multiple of a unitary map.

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Brian C. Hall, Benjamin D. Lewis. 2017-09-25. A unitary "quantization commutes with reduction" map for the adjoint action of a compact Lie group. https://arxiv.org/abs/1709.08531

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