Lie Algebra of the Lorentz group - a weird notation?

  • Thread starter Theage
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  • #1
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In Srednicki's text on quantum field theory, he has a chapter on quantum Lorentz invariance. He presents the commutation relations between the generators of the Lorentz group (equation 2.16) as follows:
$$[M^{\mu\nu},M^{\rho\sigma}] = i\hbar\Big(g^{\mu\rho}M^{\nu\sigma}-(\mu\leftrightarrow\nu)\Big)-(\rho\leftrightarrow\sigma)$$
I have never seen the strange double-arrow notation in any linear algebra book before. Is this notation at all standard and if so, what does it mean?
 

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  • #2
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It just means "its the same thing as the last term, just put [itex] \mu [/itex] instead of [itex] \nu [/itex] and vice-versa." The same about the last parenthesis.
 
  • #3
haushofer
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Indeed. The lhs should be antisymm. in mu and nu, and also in rho and sigma. That's what this notation says :)
 
  • #4
dextercioby
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A typographical convenience, nothing more. Weinberg for instance makes no LaTex shortenings.
 

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