XXXIX Workshop on Geometric Methods in Physics 27.06-3.07.2021
IX School on Geometry and Physics 21-25.06.2021

Oguzhan Kaya

Non-unitarity of the BKS transformation for symmetric spaces

We show that the BKS transformation coming from geometric quantization of the cotangent bundle of Riemannian compact symmetric spaces is not always unitary. We will use representation theory of compact Lie groups and Peter–Weyl theory to deduce a simple method to study the unitarity of the transformation. In particular, we show that for $S^5$ this transformation is not unitary. Additionally, we show that in the limit $\hbar\to 0$ (where $\hbar$ is Planck’s constant) asymptotic unitarity holds for all compact symmetric spaces.

Event sponsored by:
of Bialystok
University of Bialystok

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