Srednicki — Quantum Field Theory · Problem 93.1

Canonical Quantization of Scalar Fields — Mark Srednicki

Physics — QFT · su2-matrix-parametrization

Problem

Show that any

2\times 2

special unitary matrix

U

can be written in the form

U = a_4 + i\vec{a}\cdot\vec{\sigma}

, where

a_4

and the three-vector

\vec{a}

are real, and

\vec{a}^{\,2} + a_4^2 = 1