Freiburg 2008 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 4: Quantentheorie und Quantisierung

MP 4.2: Talk

Tuesday, March 4, 2008, 14:20–14:40, KGI-HS 1023

Wigner’s theorem - revisited. A simple proof using projective geometry. — •Kai Johannes Keller^1,2, Nikolaos A. Papadopoulos², and Andrés Fernando Reyes Lega³ — ¹II. Institut für Theoretische Physik der Universität Hamburg — ²Institut für Physik der Universität Mainz (AG THEP) — ³Universidad de los Andes, Bogotá, Colombia

This talk presents a a simple, geometric proof of Wigner’s theorem on the realization of symmetries in quantum mechanics, that clarifies its relation to projective geometry.

Although there exist several proofs, 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. The proof presented here takes a strictly geometrical point of view. 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 is simple, transparent and therefore accessible even to elementary treatments in quantum mechanics.