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Do the matrices $S^{\mu\nu}$ defined by

$$ S^{\mu\nu} = \frac{1}{4}[\gamma^\mu, \gamma^\nu] $$

have a name ($\gamma^\mu$ are the gamma matrices)? They feel very important to me since they form a representation of the Lorentz algebra, so I would like to know if there's an accepted name for them in the literature. If there's none, what would you name them?

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These are the generators of Lorentz transformations, see Peskin and Schroeder, pg. 41. $S^{ij}$ are rotation generators, and $S^{0i}$ are the boost generators.

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    $\begingroup$ I think he/she is aware of that and is after the name $\endgroup$ – Akoben Mar 10 '15 at 18:27
  • $\begingroup$ @Akoben, you're correct. This answer isn't very useful to me because I already know what the $S^{\mu\nu}$ are, I just want to know if they are commonly referred to by some term. $\endgroup$ – Koaaala Mar 11 '15 at 13:17
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I have heard it called the spin tensor or spin matrix.

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  • $\begingroup$ Any sources? (e.g., published lecture notes, journal articles, books) Or is it just something a professor said once? $\endgroup$ – Kyle Kanos Mar 10 '15 at 19:02
  • $\begingroup$ While spin matrix makes sense, it's a problematic term since the Pauli and gamma matrices are often called spin matrices as well. $\endgroup$ – Koaaala Mar 11 '15 at 13:19

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