半有限因子中保持转移概率映射的Wigner型定理
Wigner-Type Theorem on transition probability preserving maps in semifinite factors
摘要：
维格纳定理是量子力学数学表述的基石之一，它断言量子系统的每一个对称性都是幺正的或反幺正的。这个经典结果是维格纳于1931年首次给出的。此后，许多作者以各种方式证明和推广了它。最近，G. P. Gehér推广了Wigner和Molnár的定理，刻画了保持转移概率的所有秩- $n$投影在Grassmann空间上的变换。本文的目的是提供一种新的方法来描述Grassmann空间之间保持（不一定是双射）转移概率映射的一般形式。作为副产品，我们能够推广Molnár和G. P. Gehér.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
