Holomorphic Quantization in Constant Curvature Backgrounds

Dmitri Bykov; Viacheslav Krivorol

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arXiv · 2602.22984

Holomorphic Quantization in Constant Curvature Backgrounds

Dmitri Bykov·Viacheslav Krivorol

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Abstract

We present a holomorphic quantization scheme for free point particles on two-dimensional constant curvature Riemannian backgrounds. The procedure is based on a Lagrangian embedding of the particle configuration space into a product of coadjoint orbits of the background isometry group. Examples are provided by particles on the plane, torus, sphere, and hyperbolic plane, with or without a monopole field. We elaborate the method by recovering the Hamiltonian spectrum and the wave functions on such spaces. As a by-product, we obtain a geometric and physical interpretation of Repka's result on the decomposition of tensor products of $\mathbf{SL}(2,\mathbb{R})$ discrete series representations.

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Dmitri Bykov, Viacheslav Krivorol. 2026-02-26. Holomorphic Quantization in Constant Curvature Backgrounds. https://arxiv.org/abs/2602.22984

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