What Is the Hamiltonian for a Wire Coil Under Reflection Transformation?

AI Thread Summary
The discussion centers on the Hamiltonian for a wire coil subjected to reflection transformation and its implications under Noether's theorem. It highlights that while electrodynamics is invariant under spatial reflections and time reversal, electromagnetism itself is not invariant due to the behavior of magnetic fields under reflection. The transformation of electromagnetic field components is crucial for understanding these invariances. The distinction between right-handed and left-handed magnetism is emphasized, indicating that the latter does not occur in reality. Ultimately, the conversation seeks to prove the non-invariance of electromagnetism under reflection transformations.
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When applying Noether's theorem to a coil of wire under reflection transformation invariance, what Hamiltonian would one use as as the extermized function? I realize that electromagnetism is not invariant over reflection transformations, that's what I am trying to prove.
 
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Electrodyanmics is invariant under spatial reflections and time reversal. QED additionally also under charge conjugation. Of course, you have to transform the electromagnetic field components accordingly!
 
Actually, since magnetism with respect to the current through a wire is "right-handed," (\nablaxB = (1/c)\partialE/\partialt) after a spatial reflection it would be "left handed," (\nablaxB = (-1/c)\partialE/\partialt) which does not exist in the real world, which therefore means that electromagnetism is not invariant over spatial reflections.
 
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