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A Quantization on Riemann Surfaces with Projective Structure (2000)

Ben-Zvi, David ; Biswas, Indranil

Springer

Letters in mathematical physics 54 (2000), S. 73-82

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ISSN: 1573-0530

Keywords: projective structure ; symplectic structure ; quantization ; Moyal–Weyl algebra

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract Let X be a Riemann surface equipped with a projective structure. Let $$\mathcal{L}$$ be a square-root of the holomorphic cotangent bundle K X . Consider the symplectic form on the complement of the zero section of $$\mathcal{L}$$ obtained by pulling back the symplectic form on K X using the map ν ↦ ν⊗2. We show that this symplectic form admits a natural quantization. This quantization also gives a quantization of the complement of the zero section in K X equipped with the natural symplectic form.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1007650202446

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