XXXIX Workshop on Geometric Methods in Physics 28.06-4.07.2020
IX School on Geometry and Physics 22-26.06.2020

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:
University
of Bialystok
University of Bialystok






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