# Lorentz boost matrix for an arbitrary direction in terms of rapidity

We have derived the Lorentz boost matrix for a boost in the x-direction in class, in terms of rapidity which from Wikipedia is:

Assume boost is along a direction $\hat{n}=n_x \hat{i}+n_y \hat{j}+n_z \hat{k}$,

How do I generalise this to a boost in any arbitrary direction, and what is the result? Any help most appreciated.

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Just conjugate with rotation matrices. – Mark Eichenlaub Apr 6 '13 at 11:09
I have solved this problem myself, so maybe I should write an answer. Thanks anyways. – user7757 Apr 7 '13 at 5:00

## 2 Answers

Have you tried Wikipedia?

I think that is almost what you need:

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Thanks! This is what I need, but my question is how do you get is, from the lorentz boost matrices along x-, y- and z- directions? – user7757 Mar 6 '13 at 16:54

You act with an arbitrary rotation on the boost in one direction.

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Could you elaborate by editing your answer? – Manishearth Apr 6 '13 at 19:31