Griffiths Introduction to Elementary Particles · Problem 4.7

Bound States — David J. Griffiths

Physics — QFT · orthogonal-groups-reflection

Problem

Consider the matrix

\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}

. Is it in the group

O(2)

? How about

SO(2)

? What is its effect on the vector

\mathbf{A}

of Problem 4.6? Does it describe a possible rotation of the plane?