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Timaeus's answer could be correct. The $\Lambda$ matrix from your book may have been intended as a passive transformation (one that acts on the coordinate system) and you mistakenly used it as an active transformation (one that acts on the object). Alternatively, the $\Lambda$ matrix from your book may have been intended as the active transformation of a ...

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The first thing that bothers me is that for positive ${v}$ I get negative component of the velocity vector If your object was at rest then to someone moving to the right the object at rest is moving to the left in their frame. As for the second question it is same issue. Someone at rest will be moving to the left relative to someone moving faster than ...

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So, you want to diagonalize an operator on a subspace. Specifically you want diagonalize $W_f^n$, the restriction of $W_f$ to the eigen-space associated to $E_n^0$. [Since] $W_f$ doesn't depend of the proton spin, it's possible to divide by 2 the dimension of the problem ($\frac{g_n}{2} X \frac{g_n}{2}$ matrix instead of $g_n X g_n$ matrix). If an ...

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