Ever since investigations into the group representation theory of spacetime symmetries, chiefly due to Wigner and Bargmann in the 1930s and ‘40s, it has become something of a mantra in particle physics that a particle is an irreducible representation of the Poincaré group (the symmetry group of Minkowski spacetime). Call this ‘Wigner’s identification’. One may ask, in a philosophical spirit, whether Wigner’s identification could serve as something like a real definition (as opposed to a nominal definition) of ‘particle’—at least for the purposes of relativistic quantum field theory. In this talk, I aim to show that, while Wigner’s identification is materially adequate for many purposes—principally scattering theory—it does not provide a serviceable definition. The main problem, or so I shall argue, is that the regime of legitimate particle talk surpasses the constraints put on it by Wigner’s identification. I aim further to show that, at least in the case of particles with mass, a promising rival definition is available. This promising rival emerges from investigations due to Foldy in the 1950s, which I will outline. The broad upshot is that the definition of ‘particle’ may well be the same in both the relativistic and non-relativistic contexts, and draws upon not the Poincaré group (or any other spacetime symmetry group) but rather the familiar Heisenberg relations.
Philosophy of Physics Seminar Convenors for MT19: Tushar Menon, Adam Caulton and Chris Timpson