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Baker–Campbell–Hausdorff (CBH) Formula question

  1. May 14, 2014 #1
  2. jcsd
  3. May 14, 2014 #2


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    Like it says,

    The sum runs over all possible values of sn and rn, where sn + rn > 0. They apparently stand for the number of X's and Y's in the multiple commutator. (Glad I don't have to prove this! :wink:)
  4. May 14, 2014 #3
    I agree, proving it would be awful, to say to least.

    This may be a dumb question, but how do I know what the possible values of [itex]r_n[/itex] and [itex]s_n[/itex] are? I feel like I'm over-thinking this.

    For example, if I consider [itex][X,Y][/itex], then [itex]r_n=s_n=r_1=s_1=1[/itex]. If I just had the BCH formula as written by Dynkin, how would I know that [itex]r_1=s_1=1[/itex] for [itex]n=1[/itex]?
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