A Meaning of X in SU(2)XSU(2)

Tags:
1. Oct 15, 2016

munirah

From my reading, the X between SU(4)XSU(2) mean Cartesian product.

But How the way to mutiply two matrix A in SU(4) and B in SU(2).

Example the matrix

A=\begin{pmatrix} a & b &
c & d \\ e& f &
g & h \\ i & j &
k & l \\ m & n&
o & p \end{pmatrix}

and

B=\begin{pmatrix} 1 &2 \\
3 &4 \end{pmatrix}

Please show me the way to multiply SU(4)XSU(2) to form 8X8 matrix.

Thank you

Last edited: Oct 15, 2016
2. Oct 15, 2016

Staff: Mentor

B should be 2x2. Technically you can form such a product by components and express it as matrix but I don't think it is useful in any way in particle physics. The entries would be "a1", a2", "a3", "a4", "b1", "b2" and so on.

3. Oct 15, 2016

munirah

Sorry for wrong matrix. It mean, I just do the tensor product?

4. Oct 15, 2016

Staff: Mentor

Sure.

5. Oct 15, 2016

munirah

Thank you very much for helping me to solve my problem. Thank you again.thank you

6. Oct 15, 2016

Staff: Mentor

Sure? I would expect a block matrix $\begin{bmatrix}A & 0 \\ 0 & B\end{bmatrix}$.

7. Oct 15, 2016

Staff: Mentor

Representations are arbitrary, but the block matrix is probably a better model.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads for Meaning
I Mean value of the nuclear tensor operator