A Simple Constructive Proof of Wigner's Theorem

Abstract

This expository note presents a constructive proof of Wigner's theorem using only a few basic facts about Hilbert spaces, such as the existence of orthonormal bases and the Fourier decomposition of a vector. Our proof is based on a proof by Steven Weinberg found in the first volume of his series of textbooks on quantum field theory, but differs in a few places for the sake of greater simplicity and rigor.

arXiv comment6 pages; minor revisions to title, abstract, and body, added a comment on the polarization identity and simplified the last step of the proof