# nLab Wigner classification

Contents

not to be confused with Wigner's theorem

## Surveys, textbooks and lecture notes

#### Representation theory

representation theory

geometric representation theory

# 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

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).

## 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 May 16, 2019 at 17:22:35. See the history of this page for a list of all contributions to it.