Jacobian of a Lorentz transformation

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SUMMARY

The discussion focuses on deriving the Jacobian matrix for a Lorentz transformation when transitioning from frame A to frame B, specifically under a boost along the z-axis with speed beta. The Jacobian matrix is essential for converting partial derivatives between the two frames, represented as ##\frac{\partial}{\partial x'_{\mu}}## in terms of ##\frac{\partial}{\partial x_{\mu}}##. The confusion arises from the misconception that the Jacobian is equal to 1; however, it is a matrix that encapsulates the transformation properties of the coordinates between the two frames.

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  • Understanding of Lorentz transformations
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Homework Statement


I've never encountered Jacobians before, and having read up on them a bit I find the wording of the last part of this question confusing:

A set of coordinates ##x'_{\mu}## in frame B is obtained from the set ##x_{\mu}## in frame A, by boosting B w.r.t A with speed beta along the ##x_3=z## axis. Write down the Jacobian that let's you write ##\frac{\partial}{\partial x'_{\mu}}## in terms of ##\frac{\partial}{\partial x_{\mu}}##

Homework Equations

The Attempt at a Solution


I'm not really sure what I'm being asked! It sounds to me a bit like I should just write down the Jacobian, but isn't that equal to 1? That's what it looks like to me based on this:
http://farside.ph.utexas.edu/teaching/em/lectures/node114.html

Thanks for any help. :)
 
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The problem is asking for the Jacobian matrix. Both the matrix and its determinant are often referred to as the Jacobian.
 
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