On the realization of symmetries in quantum mechanics |
| |
Authors: | Kai Johannes Keller Nikolaos A Papadopoulos Andrés F Reyes-Lega |
| |
Institution: | 1.Inst. f. Physik (WA THEP),Johannes Gutenberg-Universit?t Mainz,Mainz,Germany;2.Departamento de Física,Universidad de los Andes,Bogotá,Colombia |
| |
Abstract: | The aim of this paper is to give a simple, geometric proof of Wigner’s theorem on the realization
of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several
proofs exist already, it seems that the relevance of Wigner’s theorem is not fully appreciated in general.
It is Wigner’s theorem which allows the use of linear realizations of symmetries and therefore guarantees
that, in the end, quantum theory stays a linear theory. In the present paper, we take a strictly geometrical
point of view in order to prove this theorem. It becomes apparent that Wigner’s theorem is nothing else
but a corollary of the fundamental theorem of projective geometry. In this sense, the proof presented here
is simple, transparent and therefore accessible even to elementary treatments in quantum mechanics. |
| |
Keywords: | Wigner theorem projective geometry |
本文献已被 SpringerLink 等数据库收录! |
|