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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

R2 v1 2026-06-23T04:50:34.128Z