On the Moduli of a quantized loop in P and KdV flows: Study of hyperelliptic curves as an extension of Euler's perspective of elastica I
| dc.creator | Matsutani, Shigeki | |
| dc.creator | Onishi, Yoshihiro | |
| dc.date | 1998-08-22 | |
| dc.date | 2003-05-04 | |
| dc.date.accessioned | 2026-07-07T05:25:47Z | |
| dc.date.available | 2026-07-07T05:25:47Z | |
| dc.description | Quantization needs evaluation of all of states of a quantized object rather than its stationary states with respect to its energy. In this paper, we have investigated moduli $\CMeP$ of a quantized elastica, a quantized loop with an energy functional associated with the Schwarz derivative, on a Riemann sphere $\PP$. Then it is proved that its moduli space is decomposed to a set of equivalent classes determined by flows obeying the Korteweg-de Vries (KdV) hierarchy which conserve the energy. Since the flow obeying the KdV hierarchy has a natural topology, it induces topology in the moduli space $\CMeP$. Using the topology, $\CMeP$ is classified. Studies on a loop space in the category of topological spaces $\Top$ are well-established and its cohomological properties are well-known. As the moduli space of a quantized elastica can be regarded as a loop space in the category of differential geometry $\DGeom$, we also proved an existence of a functor between a triangle category related to a loop space in {\bf Top} and that in $\DGeom$ using the induced topology. As Euler investigated the elliptic integrals and its moduli by observing a shape of classical elastica on $\CC$, this paper devotes relations between hyperelliptic curves and a quantized elastica on $\PP$ as an extension of Euler's perspective of elastica. | |
| dc.description | 64 pages, to appear Rev. Math. Phys | |
| dc.identifier | https://arxiv.org/abs/math/9808099 | |
| dc.identifier | http://arxiv.org/abs/math/9808099 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77313 | |
| dc.subject | Differential Geometry | |
| dc.title | On the Moduli of a quantized loop in P and KdV flows: Study of hyperelliptic curves as an extension of Euler's perspective of elastica I | |
| dc.type | text |