Wigner-type theorem on transition probability preserving maps in semifinite factors |
| |
Authors: | Wenhua Qian Liguang Wang Wenming Wu Wei Yuan |
| |
Institution: | 1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China;2. School of Mathematical Sciences, Qufu Normal University, Shandong 273165, China;3. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;4. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China |
| |
Abstract: | The 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. Gehér extended Wigner's and Molnár'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 Molnár and G.P. Gehér. |
| |
Keywords: | 47B49 54E40 Wigner's theorem Semifinite factor Grassmann spaces Transition probability |
本文献已被 ScienceDirect 等数据库收录! |
|