Discussion Overview
The discussion centers on the multiplication of matrices from the groups SU(4) and SU(2) to form an 8x8 matrix, specifically exploring the implications of the Cartesian product notation and the appropriate method for combining these matrices.
Discussion Character
- Technical explanation
- Debate/contested
Main Points Raised
- One participant suggests that the "X" in SU(4)XSU(2) indicates a Cartesian product and seeks clarification on how to multiply a matrix A from SU(4) with a matrix B from SU(2).
- Another participant asserts that B should be a 2x2 matrix and mentions that forming such a product by components is possible but may not be useful in particle physics.
- A participant questions whether the correct approach is to perform a tensor product instead of a straightforward multiplication.
- One response confirms the tensor product approach.
- Another participant suggests that a block matrix representation, specifically a structure like ##\begin{bmatrix}A & 0 \\ 0 & B\end{bmatrix}##, might be a more appropriate model.
- One participant notes that representations are arbitrary, but implies that the block matrix may be a better model.
Areas of Agreement / Disagreement
Participants express differing views on the method of combining the matrices, with some supporting the tensor product approach and others advocating for a block matrix representation. No consensus is reached on the best method.
Contextual Notes
There are unresolved questions regarding the utility of the proposed methods in practical applications, particularly in particle physics, and the discussion does not clarify the assumptions underlying the matrix operations.