- #1
Jimmy Snyder
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Homework Statement
This is from Ryder's QFT book, second ed. page 37. At the bottom of the page it says that the commutation relations (eqn 2.68?) are satisfied by:
[itex]K = \pm i\frac{\sigma}{2}[/itex]
However, I do not find this to be so. What am I missing?
Homework Equations
Here is one of the commutation relations that I think he means.
[itex][K_x,K_y] = -iJ_z[/itex]
The Attempt at a Solution
Using [itex]K = i\frac{\sigma}{2}[/itex], I get:
[itex][K_x,K_y] = [i\frac{\sigma_x}{2},i\frac{\sigma_y}{2}] = \frac{-1}{4}[\sigma_x,\sigma_y] = -\frac{1}{2}\sigma_z = iK_z \neq -iJ_z[/itex]
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