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

TL;DR

This paper offers a new, elementary proof of Wigner's theorem on quantum state transformations, applicable even in complex quantum field theory contexts with non-separable Hilbert spaces.

Contribution

It provides a novel, simplified proof of Wigner's theorem using elementary complex analysis, differing from traditional approaches.

Findings

Proof is elementary and accessible

Applicable to quantum field theory with non-separable Hilbert spaces

Broadens understanding of quantum state transformation symmetries

Abstract

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.