I met Wigner quite often when I was instructor in physics at Princeton University, for the academic year 1960-1961, and again when I was working with Wightman on our book, from Sept 1962 to Feb 1963. Wigner was an extremely polite man, and never preceded anyone in passing through a door. I always accepted his offer to stand back, since if I argued, and tried to get him through the door first, then a bottle-neck in the corridor would be created. He was always sympathetic to what I was trying to do in research, but it was difficult to assess whether he thought it was any good.
Wigner put the subject of relativistic quantum mechanics on a firm footing, when he showed that the relativistic wave equations of Klein and Gordon, and of Dirac, and Maxwell and Proca, were realisations of unitary representations of the Poincaré group, and so fell into his general theory of symmetry. I think that Dirac, in 1933, started to worry that his equation was not unitary, because the gamma matrices are not unitary. This might have induced Dirac to dabble with infinite-component fields, where he found some unitary irreducible representations of the homogeneous Lorentz group, a problem that was considered too difficult by mathematicians at the time.
When I was at Princeton the second time, we were shocked to receive a preprint by L. O'Raeffairtaigh, who claimed that Wigner's famous theorem on the unitary implementability of a symmetry map on projective space (the space of unit rays) was not properly proved in Wigner's book on atomic spectroscopy. How could such a junior physicist have seen more than the great Wigner? However, Wigner's argument is very short, and it is truly not easy to complete the proof. I think that Bargmann's paper (Jour. Math Phys., 1964) was written to show that there did exist a proof (of several densely argued pages) whose first few lines were similar to those in Wigner's book. Thank goodness.
For more about Wigner, see the Nobel pages, or the history pages.
Go to my HOME PAGES for links to all my publications on mathematical physics.
© by Ray Streater, 13/4/00.