An alternative proof of Wigner theorem on quantum transformations based on elementary complex analysis

Amaury Mouchet (1, 2)

1 FDP - Fédération de recherche Denis Poisson
2 LMPT - Laboratoire de Mathématiques et Physique Théorique

According to Wigner theorem, transformations of quantum states which preserve the probabilities are either unitary or antiunitary. This short communication presents an elementary proof of this theorem that significantly departs from the numerous ones already existing in the literature. The main line of the argument remains valid even in quantum field theory where Hilbert spaces are non-separable.

Mots clés: Wigner theorem; quantum transformations; unitary or antiunitary operators; théorème de Wigner

Domaines: Physique Quantique [quant-ph]

Amaury Mouchet. An alternative proof of Wigner theorem on quantum transformations based on elementary complex analysis. Physics Letters A, 2013, 377, pp.2709-2711. ⟨10.1016/j.physleta.2013.08.017⟩. ⟨hal-00807644v2⟩