An Excursion into Berezin–Toeplitz Quantization and Related Topics

Abstract

We present an introduction to the Berezin and Berezin–Toeplitz quantizations, starting from their historical origins and relationships with other quantization methods, discussing various instructive examples like the Segal–Bargmann–Fock space, and culminating by highlights of proofs of the existence of these quantizations using both the Boutet de Monvel theory and the approach via Fefferman’s expansion and Forelli–Rudin construction. The exposition strives to be reasonably self-contained and accessible to nonexperts.