A model of internal symmetry for a five-component order parameter uses the group of…

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Group theory and symmetry · Group theory and symmetry

Invariance, Ch Lie groups and Lie algebras: rotations, SU(2) and the double cover

Problem

A model of internal symmetry for a five-component order parameter uses the group

SO(5)

of real orthogonal

5\times5

matrices with determinant

+1

. Find

\dim SO(5)

by counting the independent constraints in

\mathsf{R}^{\mathsf T}\mathsf{R}=\mathsf{1}

for a general

n\times n

real matrix, then setting

n=5