Wigner's Little Groups

Why is it interesting?

Layman

Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.

Student

The little group is a subgroup of the Poincare group which leaves the four-momentum of a given particle invariant. The little groups for massive and massless particles are locally isomorphic to the three-dimensional rotation group and the two-dimensional euclidean group respectively. GAUGE TRANSFORMATIONS AS LORENTZ-BOOSTED ROTATIONS by D. HAN et. al.

A good explanation can be found at page 8 in https://indico.cern.ch/event/544849/contributions/2214530/attachments/1301154/1942518/yskim.pdf
Another great introduction is section 2 here https://arxiv.org/pdf/1709.04891.pdf
A good discussion can also be found in Groups, Physics, and Geometry by Gilmore

Researcher

The motto in this section is: the higher the level of abstraction, the better.

Common Question 1

Common Question 2

Examples

Example1

Example2:

History

https://arxiv.org/pdf/hep-th/9512151.pdf