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

  1. Oct 15, 2016 #1
    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. jcsd
  3. Oct 15, 2016 #2

    mfb

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    2016 Award

    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.
     
  4. Oct 15, 2016 #3
    Sorry for wrong matrix. It mean, I just do the tensor product?
     
  5. Oct 15, 2016 #4

    mfb

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    2016 Award

    Staff: Mentor

    Sure.
     
  6. Oct 15, 2016 #5
    Thank you very much for helping me to solve my problem. Thank you again.thank you
     
  7. Oct 15, 2016 #6

    fresh_42

    Staff: Mentor

    Sure? I would expect a block matrix ##\begin{bmatrix}A & 0 \\ 0 & B\end{bmatrix}##.
     
  8. Oct 15, 2016 #7

    mfb

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    2016 Award

    Staff: Mentor

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