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Wigner-type theorem on transition probability preserving maps in semifinite factors
Qian, Wenhua1; Wang, Liguang2; Wu, Wenming1; Yuan, Wei3,4
2019-03-15
Source PublicationJOURNAL OF FUNCTIONAL ANALYSIS
ISSN0022-1236
Volume276Issue:6Pages:1773-1787
AbstractThe Wigner's theorem, which is one of the cornerstones of the mathematical formulation of quantum mechanics, asserts that every symmetry of quantum system is unitary or anti-unitary. This classical result was first given by Wigner in 1931. Thereafter it has been proved and generalized in various ways by many authors. Recently, G.P. Geller extended Wigner's and Molnar's theorems and characterized the transformations on the Grassmann space of all rank-n projections which preserve the transition probability. The aim of this paper is to provide a new approach to describe the general form of the transition probability preserving (not necessarily bijective) maps between Grassmann spaces. As a byproduct, we are able to generalize the results of Molnar and G.P. Geher. (C) 2018 Elsevier Inc. All rights reserved.
KeywordWigner's theorem Semifinite factor Grassmann spaces Transition probability
DOI10.1016/j.jfa.2018.05.019
Language英语
Funding ProjectNational Natural Science Foundation of China[11671133] ; National Natural Science Foundation of China[11371222] ; Youth Innovation Promotion Association, CAS
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000458347000003
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32394
Collection数学所
Affiliation1.Chongqing Normal Univ, Sch Math Sci, Chongqing 401331, Peoples R China
2.Qufu Normal Univ, Sch Math Sci, Jining 273165, Shandong, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Qian, Wenhua,Wang, Liguang,Wu, Wenming,et al. Wigner-type theorem on transition probability preserving maps in semifinite factors[J]. JOURNAL OF FUNCTIONAL ANALYSIS,2019,276(6):1773-1787.
APA Qian, Wenhua,Wang, Liguang,Wu, Wenming,&Yuan, Wei.(2019).Wigner-type theorem on transition probability preserving maps in semifinite factors.JOURNAL OF FUNCTIONAL ANALYSIS,276(6),1773-1787.
MLA Qian, Wenhua,et al."Wigner-type theorem on transition probability preserving maps in semifinite factors".JOURNAL OF FUNCTIONAL ANALYSIS 276.6(2019):1773-1787.
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