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1. I am trying to do question 3 on this sheet;

http://www.maths.ox.ac.uk/system/fil.../Sheet4_13.pdf

I understand the basics, but I really don't know what they want in terms of proving it is a tensor. I have looked through every book in the library, and still have no idea. I was wondering if anyone could point me in the right direction?

- There is a standard tensor ICS transformation rule using derivatives - do they want me to show that this is equivalent to a Lorentz transformation? If so, what other way is there to Lorentz transform a tensor?
- Do they want me to show that this transformation is consistent when transforming across several ICSs?
- Do they want me to compare it to the normal Electromagnetic field tensor, which we have been told is a tensor?

There are two methods suggested on the sheet, but I want to understand the first one ideally. Any help appreciated, I'm really confused.

Also, if anyone knows of a textbook with lost of non-numerical exercises on special relativity it would be much appreciated. Our course textbook (Woodhouse, Springer) follows our lecture notes word for word, and thus is not helpful. The rest are all Physicsy.
2. (Original post by Octohedral)
I am trying to do question 3 on this sheet;

http://www.maths.ox.ac.uk/system/fil.../Sheet4_13.pdf

I understand the basics, but I really don't know what they want in terms of proving it is a tensor. I have looked through every book in the library, and still have no idea. I was wondering if anyone could point me in the right direction?

- There is a standard tensor ICS transformation rule using derivatives - do they want me to show that this is equivalent to a Lorentz transformation? If so, what other way is there to Lorentz transform a tensor?
- Do they want me to show that this transformation is consistent when transforming across several ICSs?
- Do they want me to compare it to the normal Electromagnetic field tensor, which we have been told is a tensor?

There are two methods suggested on the sheet, but I want to understand the first one ideally. Any help appreciated, I'm really confused.

Also, if anyone knows of a textbook with lost of non-numerical exercises on special relativity it would be much appreciated. Our course textbook (Woodhouse, Springer) follows our lecture notes word for word, and thus is not helpful. The rest are all Physicsy.
How do the components of the E and B fields transform?
3. (Original post by ben-smith)
How do the components of the E and B fields transform?
Using the four-potential? So we are supposed to show what F* is in a different co-ordinate system that way, and show that it agrees with the tensor transformation rule?

I'm probably being really stupid here - I just need to get it straight in my head. Thanks for your help
4. (Original post by Octohedral)
Using the four-potential? So we are supposed to show what F* is in a different co-ordinate system that way, and show that it agrees with the tensor transformation rule?

I'm probably being really stupid here - I just need to get it straight in my head. Thanks for your help
the four potential would certainly help. I'm not doing your course so it's hard for me suggest the appropriate method but you've essentially got to find how an arbitrary component transforms and show that this is the transformation law of a rank two tensor.
If you know any geometry it becomes kind of easier to see that it's a tensor because it's the hodge dual of the exterior derivative of a vector.

EDIT: wrt books, I like Landau-Lifschitz volume 2 'the classical theory of fields' for relativistic electromagnetism though you've got to be up on your lagrangians. It should be in your college library. You won't find it in blackwell's (I assume you're at Oxford) unless they've restocked because I bought the last copy
5. (Original post by ben-smith)
the four potential would certainly help. I'm not doing your course so it's hard for me suggest the appropriate method but you've essentially got to find how an arbitrary component transforms and show that this is the transformation law of a rank two tensor.
If you know any geometry it becomes kind of easier to see that it's a tensor because it's the hodge dual of the exterior derivative of a vector.

EDIT: wrt books, I like Landau-Lifschitz volume 2 'the classical theory of fields' for relativistic electromagnetism though you've got to be up on your lagrangians. It should be in your college library. You won't find it in blackwell's (I assume you're at Oxford) unless they've restocked because I bought the last copy
Thank you so much - that really helped! I'll look up the Geometry link, out of interest.

I'll look up the book too, thanks for the recommendation (if not for stealing the last copy). I'm all there with Lagrangians

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