Lorentz Boosts in the same direction should form a group. Two boosts along the x axis should produce another boost along the x axis. Is that correct?

Hagman7v 2022-09-26 Answered
Lorentz Boosts in the same direction should form a group. Two boosts along the x axis should produce another boost along the x axis. Is that correct?
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vyhlodatis
Answered 2022-09-27 Author has 14 answers
Yes, it is a one-dimensional subgroup generated by exponentiating an infinitesimal boost. Every one dimensional exponentiation of a generator forms an abelian group, because e a G e b G = e ( a + b ) G there is nothing to not commute. This result is the addition of velocities, you can explicity check that this is associative (it is always manifestly commutative).
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