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Please help with notation

  1. Nov 19, 2014 #1
    The symbol for a Lorentz transformation is sometimes Λαβ and sometimes Λμν.

    When Λαβ is shown by a matrix, the upper index denotes the entries in the rows and the lower index denotes the entries in the columns.

    When Λμν is shown by a matrix, does the upper index still denotes the entries in the rows?

    Any help is much appreciated.

    Thanks.
     
  2. jcsd
  3. Nov 19, 2014 #2

    Orodruin

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    This depends on how you chose to represent the Lorentz transformation in matrix form, or more precisely, how you chose to represent covariant and contravariant vectors and how the Lorentz transformation acts on them.
     
  4. Nov 19, 2014 #3
    Does it mean that when Λαβ acts on a contravariant vector xβ, then the upper index of Λ denotes the rows and when Λαβ acts on a covariant vector xβ, then it is the lower index which denotes the rows?
     
  5. Nov 19, 2014 #4

    dextercioby

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    Yes, that's an accepted logic. Just remember that physicists don't put mu exactly over nu, it's always a space (it's either south-west-north-east or north west-south east, but never north south).
     
  6. Nov 19, 2014 #5

    Matterwave

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    I'd like to also add that usually I see a prime on one of the indices to make it easier to figure out which frame to which the Lorentz transformation is transforming to.
     
  7. Nov 20, 2014 #6
    Thanks for all the replies!

    Yes, 'Matterwave', I intended to put a prime on one of the indices of Λ to distinguish from which frame of reference and to which frame the Λ is transforming but I could not figure out the way to do it!
     
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