Discussing the mathematical formalism of generators (Lorentz Group)

Click For Summary
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.
 
Physics news on Phys.org
  • #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: .
 
  • Like
Likes vanhees71 and PeroK

Similar threads

Undergrad Generators of translations
  • · Replies 0 ·
Replies
0
Views
2K
Graduate Show Lagrangian is invariant under a Lorentz transformation without using generators
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Lorentz Transformations and Angular momentum | Tong's QFT notes
  • · Replies 6 ·
Replies
6
Views
2K
Poincare group representations
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Understanding Lorentz Groups and some key subgroups
  • · Replies 3 ·
Replies
3
Views
2K
Bjorken Drell derivation - Lorentz transformation
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Is the Higgs Field Responsible for Microscopic Gravitational Effects?
  • · Replies 24 ·
Replies
24
Views
3K
QFT: Lorentz Trans+ Field infinitesimal variation
  • · Replies 15 ·
Replies
15
Views
3K
Why is (1/2,1/2) the vector representation?
  • · Replies 8 ·
Replies
8
Views
6K
Deriving the commutation relations of the Lie algebra of Lorentz group
  • · Replies 3 ·
Replies
3
Views
3K