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11.
12.
Modulo some natural generalizations to noncompact spaces, we show in this Letter that Moyal planes are nonunital spectral triples in the sense of Connes. The action functional of these triples is computed, and we obtain the expected result, i.e. the noncommutative Yang–Mills action associated with the Moyal product. In particular, we show that Moyal gauge theory naturally fits into the rigorous framework of noncommutative geometry. 相似文献
13.
M. Castagnino R. Id Betan R. Laura 《International Journal of Theoretical Physics》2003,42(10):2423-2439
By extending the notion of mixed states to functionals acting on the space of observables with diagonal singularity we obtain a well-defined complex spectral decomposition of the time evolution for a quantum decaying system. In this formalism, generalized Gamow states are obtained with well-defined physical properties. 相似文献
14.
Song LI Guo Mao WANG Zhi Song LIU 《数学学报(英文版)》2005,21(6):1475-1486
The purpose of this paper is to investigate the mean size formula of wavelet packets in Lp for 0 〈 p ≤ ∞. We generalize a mean size formula of wavelet packets given in terms of the p-norm joint spectral radius and we also give some asymptotic formulas for the Lp-norm or quasi-norm on the subdivision trees. All results will be given in the general setting, 相似文献
15.
Hubert Grudziński 《Reports on Mathematical Physics》2004,53(2):317-328
The eigenvalues and eigenfunctions of an elementary 3-fermion 2-body operator 3P2g∧I1A3∑1≤i≤j≤3P2g(i, j)A3 acting on a 3-particle antisymmetric finite-dimensional Hilbert space have been found. Here Pg2 denotes the projection operator onto a 2-particle antisymmetric function g2, while A3 denotes the 3-particle antisymmetrizing operator. 相似文献
16.
In this paper we continue to study the spectral norms and their completions ([4]) in the case of the algebraic closure $ \overline {\mathbb Q} $ of ? in ?. Let $ \widetilde{\overline{\mathbb{Q}}} $ be the completion of $ \overline {\mathbb Q} $ relative to the spectral norm. We prove that $ \widetilde{\overline{\mathbb{Q}}} $ can be identified with the R‐subalgebra of all symmetric functions of C(G), where C(G) denotes the ?‐Banach algebra of all continuous functions defined on the absolute Galois group G = Gal$ {\overline {\mathbb Q}} / {\mathbb Q} $. We prove that any compact, closed to conjugation subset of ? is the pseudo‐orbit of a suitable element of $ \widetilde{\overline{\mathbb{Q}}} $. We also prove that the topological closure of any algebraic number field in $ \widetilde{\overline{\mathbb{Q}}} $ is of the form $\widetilde{\mathbb{Q}[x]}$ with x in $ \widetilde{\overline{\mathbb{Q}}} $. 相似文献
17.
Based on the Fourier transform method, a simple closed-form expression for the on-axis power spectrum of ultrashort Gaussian pulsed beams in diffraction at a circular aperture is derived, which permits us to study spectral changes both analytically and numerically. It is shown that for diffracted pulsed beams there exist spectral red and blue shifts, spectral narrowing, and spectral switches in the near field. The aperture diffraction plays an important role in spectral switching, but both the truncation parameter and bandwidth (or equally, Fourier transform limited pulse duration) affect the behavior of spectral switches. 相似文献
18.
We characterize all equivariant odd spectral triples for the quantum SU(2) group acting on its L
2-space and having a nontrivial Chern character. It is shown that the dimension of an equivariant spectral triple is at least three, and given any element of the K-homology group of SUq(2), there is an equivariant odd spectral triple of dimension 3 inducing that element. The method employed to get equivariant spectral triples in the quantum case is then used for classical SU(2), and we prove that for p < 4, there does not exist any equivariant spectral triple with nontrivial K-homology class and dimension p acting on the L
2-space.The first author would like to acknowledge support from the National Board of Higher Mathematics, India. 相似文献
19.
20.
Alexander Yu. Gelfgat 《国际流体数值方法杂志》2004,44(2):135-146
The global Galerkin method is applied to the benchmark problem that considers an oscillatory regime of convection of air in a tall two‐dimensional rectangular cavity. The three most unstable modes of the linearized system of the Boussinesq equations are studied. The converged values of the critical Rayleigh numbers together with the corresponding oscillation frequencies are calculated for each mode. The oscillatory flow regimes corresponding to each of the three modes are approximated asymptotically. No direct time integration is applied. Good agreement with the previously published results obtained by solution of the time‐dependent Boussinesq equations is reported. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献