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Lie Algebra of the Lorentz group - a weird notation?

  1. Dec 13, 2014 #1
    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?
  2. jcsd
  3. Dec 13, 2014 #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.
  4. Dec 13, 2014 #3


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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 :)
  5. Dec 13, 2014 #4


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    A typographical convenience, nothing more. Weinberg for instance makes no LaTex shortenings.
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