Jacobian of a Lorentz transformation

The matrix relates the partial derivatives of the coordinates in frame A to the partial derivatives of the coordinates in frame B. It is not equal to 1, but rather has a specific form that involves the speed beta and the direction of the boost along the z-axis.
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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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1. What is the Jacobian of a Lorentz transformation?

The Jacobian of a Lorentz transformation is a mathematical term that refers to the determinant of the matrix representing the transformation. It is used to calculate the change in a function's value caused by a transformation.

2. How is the Jacobian of a Lorentz transformation related to special relativity?

The Jacobian of a Lorentz transformation is closely related to special relativity because it is used to map between different reference frames in spacetime. It helps to calculate the effects of time dilation and length contraction on physical quantities.

3. Can the Jacobian of a Lorentz transformation be negative?

Yes, the Jacobian of a Lorentz transformation can be negative. It depends on the direction of the transformation and the orientation of the coordinate system. A negative Jacobian indicates a change in orientation or handedness of the coordinate system.

4. How is the Jacobian of a Lorentz transformation calculated?

The Jacobian of a Lorentz transformation is calculated by taking the determinant of the matrix representing the transformation. This can be done using various methods, such as using the Leibniz formula or using row reduction to find the determinant.

5. Why is the Jacobian of a Lorentz transformation important in physics?

The Jacobian of a Lorentz transformation is important in physics because it helps to understand the effects of special relativity on physical quantities. It is used in many areas of physics, including electromagnetism, quantum mechanics, and general relativity.

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