共查询到20条相似文献,搜索用时 0 毫秒
1.
2.
3.
Jonathan Weitsman 《Communications in Mathematical Physics》1992,145(3):425-433
We prove that the moduli space of flatSU(2) connections on a Riemann surface has a real polarization, that is, a foliation by lagrangian subvarieties. This polarization may provide an alternative quantization of the Chern-Simons gauge theory in higher genus, in line with the results of [11] for genus one.Supported by NSF Mathematical Sciences Postdoctoral Research Fellowship DMS 88-07291 相似文献
4.
We consider the canonical symplectic structure on the moduli space of flatg-connections on a Riemann surface of genusg withn marked points. Forg being a semisimple Lie algebra we obtain an explicit efficient formula for this symplectic form and prove that it may be represented as a sum ofn copies of Kirillov symplectic form on the orbit of dressing transformations in the Poisson-Lie groupG
* andg copies of the symplectic structure on the Heisenberg double of the Poisson-Lie groupG (the pair (G, G
*) corresponds to the Lie algebrag).Supported by Swedish Natural Science Research Council (NFR) under the contract F-FU 06821-304Supported in part by a Soros Foundation Grant awarded by the American Physical Society 相似文献
5.
We explain the bundle structures of the Determinant line bundle and the Quillen determinant line bundle considered on the connected component of the space of Fredholm operators including the identity operator in an intrinsic way. Then we show that these two are isomorphic and that they are non-trivial line bundles and trivial on some subspaces. Also we remark a relation of the Quillen determinant line bundle and the Maslov line bundle. 相似文献
6.
7.
We give a simple derivation of the spectrum of the Dirac magnetic monopole on a unit sphere S2 based on geometric quantization and the Frobenius reciprocity formula. The starting point is the calculation by Novikov and Schmelzer of the canonical symplectic structure on the coadjoint orbits of the isometry group of 3-dimensional Euclidean space E(3), which showed the appearance of the Dirac magnetic term. 相似文献
8.
Let (M, ) be a Hamiltonian U(n)-space with proper moment map. In the case where n = 1, Lerman constructed a one-parameter family of Hamiltonian U(1)-spaces M
called the symplectic cuts of M. We generalize this construction to Hamiltonian U(n) spaces. Motivated by recent theorems that show that 'quantization commutes with reduction,' we next give a definition of geometric quantization for noncompact Hamiltonian G-spaces with proper moment map, and use our cutting technique to illustrate the proof of existence of such quantizations in the case of U(n) spaces. We then show (Theorem 1) that such quantizations exist in general. 相似文献
9.
10.
T. Wurzbacher 《Journal of Geometry and Physics》1990,7(4):537-552
We study the relation between multiplicity-free symplectic manifolds and the multiplicities of group representations obtained by geometric quantization. With the help of a general equivalence theorem we can prove a conjecture of Guillemin and Sternberg in the compact Kähler case. 相似文献
11.
For a simply connected, compact, simple Lie group G, the moduli space of flat G-bundles over a closed surface Σ is known to be pre-quantizable at integer levels. For non-simply connected G, however, integrality of the level is not sufficient for pre-quantization, and this paper determines the obstruction–namely a certain cohomology class in H3(G2;Z)–that places further restrictions on the underlying level. The levels that admit a pre-quantization of the moduli space are determined explicitly for all non-simply connected, compact, simple Lie groups G. 相似文献
12.
13.
A local index theorem for families of
-operators on Riemann surfaces with functures is proved. A new Kähler metric on the moduli space of punctured surfaces is described in terms of the Eisenstein-Maass series. 相似文献
14.
Arthur Jaffe Slawomir Klimek Andrzej Lesniewski 《Communications in Mathematical Physics》1989,126(2):421-431
We formulate reflection positivity for meromorphic functions and for 1-forms on a Riemann surface. This construction yields representations of the Heisenberg algebra on a Riemann surface.Supported in part by the Department of Energy under Grant DE-FG02-88ER25065 相似文献
15.
Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space 下载免费PDF全文
We study quantum–classical correspondence in terms of the coherent wave functions of a charged particle in two- dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 2π-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic. 相似文献
16.
17.
Jae-Kwan Shim 《Journal of Geometry and Physics》2003,44(4):475-480
In this paper, we address one of the questions raised by Rieffel in his collection of questions on deformation quantization. The question is whether the K-theory groups remain the same under flabby strict deformation quantizations. By “deforming” the question slightly, we produce a negative answer to the question. 相似文献
18.
Yoshimasa Nakamura 《Letters in Mathematical Physics》1990,20(2):135-140
A nonlinear integrable flow of the Lax-type on the framed moduli space of SU(n) Yang-Mills instantons is found. 相似文献
19.
D. N. Aristov 《JETP Letters》1999,70(6):410-414
The Landau quantization for the electron gas on the surface of a sphere is considered. It is shown that in the regime of strong
fields the lowest energy states are those with magnetic quantum numbers m of order of Φ /Φ0, the number of magnetic flux quanta piercing the sphere. For an electron gas of low density (semiconducting situation) it
leads to the formation of an electronic stripe on the equator of the sphere in high fields.
Pis’ma Zh. éksp. Teor. Fiz. 70, No. 6, 405–409 (25 September 1999)
Published in English in the original Russian journal. Edited by Steve Torstveit. 相似文献
20.
As a nonrelativistic particle constrained to remain on an(N?1)-dimensional((N≥2))hypersurface embedded in an N-dimensional Euclidean space,two different components pi and pj(i,j=1,2,3,...N)of the Cartesian momentum of the particle are not mutually commutative,and explicitly commutation relations[p^i,p^j](≠0) depend on products of positions and momenta in uncontrollable ways.The generalized Dupin indicatrix of the hypersurface,a local analysis technique,is utilized to explore the dependence of the noncommutativity on the curvatures around a local point of the hypersurface.The first finding is that the noncommutativity can be grouped into two categories;one is the product of a sectional curvature and the angular momentum,and another is the product of a principal curvature and the momentum.The second finding is that,for a small circle lying a tangential plane covering the local point,the noncommutativity leads to a rotation operator and the amount of the rotation is an angle anholonomy;and along each of the normal sectional curves centering the given point the noncommutativity leads to a translation plus an additional rotation and the amount of the rotation is one half of the tangential angle change of the arc. 相似文献