一类Uhlhorn-Wigner定理的推广(英文)

A Generalization of Uhlhorn's Version of Wigner's Theorem

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摘要投影算子集合是量子力学理论中的重要概念之一.利用几何平均值单调内积得到了量子力学基本定理之一Uhlhorn-Wigner定理在投影算子集合上的一类推广. Certain operator structures play a fundamental role in the theory of quantum me- chanics, such as the set of projections. In this paper, we give an analogue of Uhlhorn＇s version of Wigner＇s theorem on such operator structures for the monotone inner product associated with geometric mean.

作者贺衎侯晋川

机构地区太原理工大学

出处《数学研究》 CSCD 2012年第2期107-114,共8页 Journal of Mathematical Study

基金 supported by NSFC(11171249,11126127)

关键词 Uhlhorn-Wigner定理单调内积投影算子 Wigner＇s theorem Monotone inner products Projections

分类号 O177 [理学—基础数学] O413.1 [理学—理论物理]

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1U Uhlhorn. Representation of symmetry transformations in quantum mechanics. Ark Fysik, 23(1963): 307-340.
2P M Van den Broek. Group representations in indefinite metric spaces. J Math Phys, 25(1984): 1205-1210.
3P M Van den Broek. Symmetry transformations in indefinite metric spaces: A genera- lization of Wigner's theorem. Physica A: Statistical and Theoretical Physics, 127(1984): 599-612.
4Cvetkovid D, Rowlinson P, Simid S K. Signless Laplacian of finite graphs. Linear Al- gebra Appl, 423(2007): 155-171.
5L Molndr. A generalization of Wigner's unitary-antiunitary theorem to Hilbert modu- les. J Math Phys, 40(1999): 5544-5554.
6L Molnair. A Wigner-type theorem on symmetry transformations in type Ⅱ factor. Int J Theor Phys, 39(2000): 1463-1466.
7L Molnar. Orthogonality preserving transformations on indefinite inner product spa- ces: generalization of Uhlhorn's version of Wigner's theorem. J Funct Anal,194(2002): 248-262.
8L Molnar. Maps on the n-dimensional subspaces of a Hilbert space preserving principalangles. Proc Amer Math Soc, 136(2008): 3205-3209.
9S Schreckenberg. Symmetry and history quantum theory: An analog of Wigner's the- orem. J Math Phys, 37(1996): 6086-6105.
10I Bengtsson, K Zyczkowski. Geometry of Quantum States: An Introduction to Quan- tum Entanglement. Cambridge University Press, Cambridge, 2006.

1贺衎,侯晋川.Wigner定理的一类推广[J].数学物理学报（A辑）,2011,31(6):1633-1636.

数学研究

2012年第2期

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一类Uhlhorn-Wigner定理的推广(英文)

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