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advanced_tools:group_theory:so_2

SO(2)

Intuitive

The Lie group $SO(2)$ describes all possible 2D rotations. The group is one dimensional, that is, it has only one parameter: the rotation angle.

The group $SO(2)$ is isomorphic to $U(1)$.

Concrete

Representations

The diagram below shows the (2-dimensional) defining representation of $SO(2)$ in its upper branch and a 4-dimensional, reducible representation of the same group in the lower branch. For a more detailed explanation of this diagram and representations of other Lie groups see Fun with Symmetry.

so2_2d_4d_reps.jpg

Abstract

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

Why is it interesting?

advanced_tools/group_theory/so_2.txt · Last modified: 2020/12/12 23:51 by edi