A Simple Constructive Proof of Wigner's Theorem
Mathematical Physics
2022-08-16 v2 math.MP
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.
Keywords
Cite
@article{arxiv.1810.10111,
title = {A Simple Constructive Proof of Wigner's Theorem},
author = {Daniel D. Spiegel},
journal= {arXiv preprint arXiv:1810.10111},
year = {2022}
}
Comments
6 pages; minor revisions to title, abstract, and body, added a comment on the polarization identity and simplified the last step of the proof