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Can the lorentz group be covered by single-parameter subgroups?

  1. Sep 11, 2010 #1
    we all know the lorentz group is of four disconnected components

    about the component connected to the unit element,

    is it coverable with single-parameter subgroups?

    put it in another way

    are all the elements in this component of the form exp(A)?

    i am studying relativistic quantum mechanics, and i find that most textbooks take this to be guaranteed.
     
  2. jcsd
  3. Sep 12, 2010 #2
    No; the Lorentz algebra is six-dimensional. Yes, you can write any element in the connected-to-the-identity part of the Lorentz group in the form e^{i theta^a T^A}.
     
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