Abstract
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.
Lingua originale | Inglese |
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pagine (da-a) | 99-112 |
Numero di pagine | 14 |
Rivista | Journal of Geometry and Physics |
Volume | 27 |
Stato di pubblicazione | Pubblicato - 1998 |
Keywords
- quantum vortex theory, Riemann surfaces, geometric quantization