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Special Relativity 4-tensor

  • Thread starter jeckster
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Homework Statement


prove the zero component lemma for any anti-symmetric 4-tensor: If any one of its 0ff-diagonal component is zero in all inertial coordinate system, then the entire tensor is zero.


Homework Equations





The Attempt at a Solution



in case of 4-vector, if a particular component is zero in all inertial frame then by Lorentz Transformation in different direction, it can be proved that the 4-vector is zero in all inertial frame.
Here, i m confusing in how to prove it in case of anti-symmetric 4-tensor

Any help would be highly appreciated. thank

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
I have the same problem. No answers yet.
off diagonal components of the antisymmetric 4 tensors in special relativity involves 3 vectors and we can form 4 vectors from them. If any component of that 3 vector is zero under LT the 4-vector is zero then all the off-diagonal terms are zero. This is what I thought but how can I express this in Mathematical Language?
If I'm wrong can you give me a clue about it?
 

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