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The pure state space of Quantum Mechanics is investigated as Hermitian Symmetric Kähler manifold. The classical principles of quantum mechanics (Quantum Superposition Principle, Heisenberg Uncertainty Principle, Quantum Probability Principle) and Spectral Theory of observables are discussed in this non-linear geometrical context. 相似文献
4.
Daniel C. Cohen Peter Orlik 《Transactions of the American Mathematical Society》2005,357(8):3031-3050
We study the Gauss-Manin connection for the moduli space of an arrangement of complex hyperplanes in the cohomology of a complex rank one local system. We define formal Gauss-Manin connection matrices in the Aomoto complex and prove that, for all arrangements and all local systems, these formal connection matrices specialize to Gauss-Manin connection matrices.
5.
I. Nakai 《Commentarii Mathematici Helvetici》1998,73(2):177-205
A curvilinear d-web W = (F
1 , . . . , F
d
) is a configuration of d curvilinear foliations F
i
on a surface. When d = 3, Bott connections of the normal bundles of F
i
extend naturally to equal affine connection, which is called Chern connection. For 3 < d, this is the case if and only if the modulus of tangents to the leaves of F
i
at a point is constant. A d-web is associative if the modulus is constant and weakly associative if Chern connections of all 3-subwebs have equal curvature form. We give a geometric interpretation of the curvature form
in terms of fake billiard in §2, and prove that a weakly associative d-web is associative if Chern connections of triples of the members are non flat, and then the foliations are defined by members
of a pencil (projective linear family of dim 1) of 1-forms. This result completes the classification of weakly associative
4-webs initiated by Poincaré, Mayrhofer and Reidemeister for the flat case. In §4, we generalize the result for n + 2-webs of n-spaces.
Received: September 23, 1996 相似文献
6.
Zhu Da xin 《数学年刊B辑(英文版)》1994,15(3):293-298
ACOMPLETEMETRICOFPOSITIVECURVATUREONR~nANDEXISTENCEOFCLOSEDGEODESICS¥ZHUDAXIN(DepartmentofMathematics,TianjinUniversitylTianj?.. 相似文献
7.
WU Ke ZHAO Weizhong & GUO Hanying Department of Mathematics Capital Normal University Beijing China Institute of Theoretical Physics Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2006,(11)
In a way similar to the continuous case formally, we define in different but equivalent manners the difference discrete connection and curvature on discrete vector bundle over the regular lattice as base space. We deal with the difference operators as the discrete counterparts of the derivatives based upon the differential calculus on the lattice. One of the definitions can be extended to the case over the random lattice. We also discuss the relation between our approach and the lattice gauge theory and apply to the discrete integrable systems. 相似文献
8.
本文证明了Hopf主纤维丛S^3的几个相关的命题,指出底流形S^3上的Laplace算子在主丛上的提升是主丛S^3上的Laplace算子,以及主丛的嵌入截面具有不动点性质等。 相似文献
9.
Some curvature conditions about the geodesics emanating from a submanifold are obtained. These conditions are used to to study the topological and geometric properties of the ambient spaces which admit some minimal submanifolds. 相似文献
10.
Patrizio Frosini 《Geometriae Dedicata》2004,108(1):105-110
In this paper we prove that for every real-valued Morse function φ on a smooth closed manifold ℳ and every neighborhood U of its critical points a suitable Riemannian metric μ
U
exists such that φ is linear outside
U 相似文献