- #1

- 17

- 0

## Main Question or Discussion Point

From Gauge Theory of particle physics, Cheng and Li I dont understand the flollowing:

"Given any two groups G={g1,..} H= {h1,h2,...}

if the g's commute with the h's we can define a direct product group G x H={[tex]g_ih_j[/tex]} with the multplication law:

[tex]g_kh_l . g_mh_n = g_kh_m . h_lh_n[/tex]

Examples of direct product groups are SU(2) x U(1) ( the group consists of elements which are direct products of SU(2) matrices and the U(1) phase factor) and

SU(3) x SU(3) (the group consists of elements which are direct products of matrices of two different SU(3)'s."

My question is: You need the g's and h's to commute. I can see how SU(2) and U(1) elements can commute. I dont see how an element of SU(3) commutes with

another SU(3) element?

"Given any two groups G={g1,..} H= {h1,h2,...}

if the g's commute with the h's we can define a direct product group G x H={[tex]g_ih_j[/tex]} with the multplication law:

[tex]g_kh_l . g_mh_n = g_kh_m . h_lh_n[/tex]

Examples of direct product groups are SU(2) x U(1) ( the group consists of elements which are direct products of SU(2) matrices and the U(1) phase factor) and

SU(3) x SU(3) (the group consists of elements which are direct products of matrices of two different SU(3)'s."

My question is: You need the g's and h's to commute. I can see how SU(2) and U(1) elements can commute. I dont see how an element of SU(3) commutes with

another SU(3) element?