# nLab Wigner classification

not to be confused with Wigner's theorem

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## Surveys, textbooks and lecture notes

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• Axiomatizations

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# Contents

## Idea

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

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

## References

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 $U_{(-)}$ are those for which all the maps $g \mapsto \langle \Phi \vert U_g \Psi \rangle$ 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

Review includes

Last revised on December 28, 2017 at 17:36:37. See the history of this page for a list of all contributions to it.