nLab Wigner classification


not to be confused with Wigner's theorem



physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics

Representation theory



The identification of particle species with irreducible unitary representations of the symmetry group acting on matter fields over spacetime. Named after Eugene Wigner.

For details see at

It uses a method that goes back to Frobenius and came to be known as “Wigner’s little group method” or the “Mackey machine” (Mackey 68).


The original article is

  • Eugene Wigner, On unitary representations of the inhomogeneous Lorentz group, Annals of Mathematics, 40 (1939) 149–204

The observation that Wigner’s representations U ()U_{(-)} are those for which all the maps gΦ|U gΨg \mapsto \langle \Phi \vert U_g \Psi \rangle are measurable and their correspondence of irreducible unitary representations to induced representations of irreps of the stabilizer group of a given momentum is (e.g. Dragon 16) due to

  • George Mackey, Induced Representations of Groups and Quantum Mechanics, W. A. Benjamin, New York, 1968


Last revised on March 10, 2024 at 14:17:39. See the history of this page for a list of all contributions to it.