Remarks on quantum vortex theory on Riemann surfaces

Mauro Spera, Vittorio Penna

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Quantized point vortex theories on a compact Riemann surface of arbitrary genus (in the zero total vorticity case) are investigated. By taking meromorphic functions thereon as order parameters and resorting to the Weil-Kostant, Abel, Riemann and Riemann-Roch theorems, a natural phase space and Hamiltonian for the vortex-antivortex configurations is exhibited, leading to explicit vortex-antivortex coherent states wave functions via geometric quantization. Furthermore, a relationship between point and smooth vorticities is established by means of Green functions associated to divisors on a Riemann surface and Poincare duality, thereby yielding a natural regularization of the singular theory.
Original languageEnglish
Pages (from-to)99-112
Number of pages14
JournalJournal of Geometry and Physics
Publication statusPublished - 1998


  • quantum vortex theory, Riemann surfaces, geometric quantization


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