Discussing the mathematical formalism of generators (Lorentz Group)

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The discussion centers on the mathematical formalism of the Lorentz group, which encompasses rotations and boosts that adhere to the Lorentz condition. Participants explore the representation of this group through matrices, specifically how infinitesimal transformations relate to generators of the group. The Baker-Campbell-Hausdorff formula is highlighted as a crucial tool for expressing compositions of transformations as exponentials of generators. There is a focus on understanding specific equations related to transformations and the implications of commutation relations between boosts and rotations. Overall, the conversation aims to clarify the mathematical foundations underlying Lorentz transformations and their representations.
  • #31
samalkhaiat said:
Rotations or non-rotations, by the object (M_{\alpha \beta})^{\mu}{}_{\nu}, we always mean the (\mu\nu) matrix elements of the matrix M_{\alpha \beta}.

Alright, so the upper index refers to rows and the lower to columns always. Thanks for the clarification.
 
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  • #32
PeroK said:
[...] the Baker-Campbell-Hausdorf formula [...]

I've found a reliable source about the Baker-Campbell-Hausdorf formula: problem 3 here. The solution is here :smile: .
 
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