排序方式: 共有7条查询结果,搜索用时 31 毫秒
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We study the geometry of determinant line bundles associated with Dirac operators on compact odd-dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the commutator anomaly formula using a construction based on noncyclic trace extensions and associated nonmultiplicative renormalized determinants. 相似文献
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Eigenvalue-Dynamics off the Calogero–Moser System 总被引:1,自引:1,他引:0
By finding N(N– 1)/2 suitable conserved quantities, free motions of real symmetric N×N matrices X(t), with arbitrary initial conditions, are reduced to nonlinear equations involving only the eigenvalues of X – in contrast to the rational Calogero-Moser system, for which [X(0),Xd(0)] has to be purely imaginary, of rank one. 相似文献
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Joakim Arnlind Martin Bordemann Jens Hoppe Choonkyu Lee 《Letters in Mathematical Physics》2008,84(1):89-98
We describe the Hamiltonian reduction of a time-dependent real-symmetric N×N matrix system to free vector dynamics, and also provide a geodesic interpretation of Ruijsenaars–Schneider systems. The simplest
of the latter, the goldfish equation, is found to represent a flat-space geodesic in curvilinear coordinates.
相似文献
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Joakim Arnlind Martin Bordemann Laurent Hofer Jens Hoppe Hidehiko Shimada 《Communications in Mathematical Physics》2009,288(2):403-429
We introduce C-Algebras of compact Riemann surfaces as non-commutative analogues of the Poisson algebra of smooth functions on . Representations of these algebras give rise to sequences of matrix-algebras for which matrix-commutators converge to Poisson-brackets
as N → ∞. For a particular class of surfaces, interpolating between spheres and tori, we completely characterize (even for the
intermediate singular surface) all finite dimensional representations of the corresponding C-algebras. 相似文献
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A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. We prove that there exists a unique metric and torsion-free connection that is compatible with the complex structure, and the curvature is explicitly calculated. A noncommutative analogue of the fact that the catenoid is a minimal surface is studied by constructing a Laplace operator from the connection and showing that the embedding coordinates are harmonic. Furthermore, an integral is defined and the total curvature is computed. Finally, classes of left and right modules are introduced together with constant curvature connections, and bimodule compatibility conditions are discussed in detail. 相似文献
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We define noncommutative minimal surfaces in the Weyl algebra, and give a method to construct them by generalizing the well-known Weierstrass representation. 相似文献
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We show that the pseudo-Riemannian geometry of submanifolds can be formulated in terms of higher order multi-linear maps. In particular, we obtain a Poisson bracket formulation of almost (para-)Kähler geometry. 相似文献
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