Prove commutation relation of galilei boosts and rotations

  • Thread starter ma18
  • Start date
  • #1
93
1

Homework Statement


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

Homework 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


The Attempt at a Solution


[/B]
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.
 

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Answers and Replies

  • #2
DrDu
Science Advisor
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What do you mean with expanded form?
 
  • #3
93
1
What do you mean with expanded form?
The taylor expansion
 
  • #4
DrDu
Science Advisor
6,048
766
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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