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Prove commutation relation of galilei boosts and rotations

  1. Oct 28, 2015 #1
    1. The problem statement, all variables and given/known data
    Use the formulas given (which have been solved in previous questions) prove that

    upload_2015-10-28_7-14-0.png

    where w_12 is a complex constant.

    From here, induce that

    upload_2015-10-28_7-13-29.png

    where eps_abc is the fully anti-symmetric symbol

    2. Relevant equations

    The equations given to use are:

    upload_2015-10-28_7-12-46.png

    upload_2015-10-28_7-12-56.png

    upload_2015-10-28_7-13-7.png

    3. The attempt at a solution

    First, I expanded the commutator given (cannot give here as I have reached max file upload for a single post), but after that I keep on looking at it and I'm not exactly sure how to proceed. I have proved the first and last of the "relevant equations" and have the expanded forms of that and I think I may have to use that but I am not sure.

    Any help would be appreciated.
     

    Attached Files:

    Last edited: Oct 28, 2015
  2. jcsd
  3. Oct 29, 2015 #2

    DrDu

    User Avatar
    Science Advisor

    What do you mean with expanded form?
     
  4. Nov 11, 2015 #3
    The taylor expansion
     
  5. Nov 12, 2015 #4

    DrDu

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    Science Advisor

    From the Taylor expansion of the last equation you gave, the second equation should follow directly given that epsilon is an arbitrary constant.
     
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