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.
|Number of pages||14|
|Journal||Journal of Geometry and Physics|
|Publication status||Published - 1998|
- quantum vortex theory, Riemann surfaces, geometric quantization