"An elementary particle ‘is’ an irreducible representation"

A well-known particle physicist’s adage:

Ever since the fundamental paper of Wigner on the irreducible representations of the Poincaré group, it has been a (perhaps implicit) definition in physics that an elementary particle ‘is’ an irreducible representation of the group, G, of ‘symmetries of nature’ (Ne’eman and Sternberg 1991, pp. 327.) 

But what exactly does that mean? Many would agree that Wigner’s seminal work on the Poincaré group has some deep metaphysical implication. But what? Wigner himself provided very little indication as to what it might be, even in his later work in the philosophy of physics.

However, there seems to be what Arthur Fine would call a “core position” about Wigner’s result. That is: there is a tight mathematical connection between the symmetry groups of nature, and the measurable quantities of quantum theory. You can even diagram it:

However, as I’ve argued before (and in a forthcoming article), a certain realist addition to this core position just doesn’t make sense. So what, if anything, can be said about Wigner’s result beyond the core position?

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2 thoughts on “"An elementary particle ‘is’ an irreducible representation"

  1. Chris Pincock

    Bryan, congratulations on the paper — I will look forward to reading it. My vague sense of this talk is that a necessary condition on being an elementary particle is that there is this sort of associated representation. And I guess your diagram also fits with this way of thinking about the situation. But this doesn’t support any kind of identification or ontic structural realism, I hope!

  2. Bryan

    Hi Chris! If this kind of connection fits your ideas on representation as well, all the better. Minimally, I’ll be satisfied to locate any kind of “natural ontological attitude” in this situation — I’m just not yet sure what it is.