Hamiltonian for a wire coil under reflection transformation

[zush]

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.

 

[vanhees71]

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!

 

[zush]

Actually, since magnetism with respect to the current through a wire is "right-handed," ($$\nabla$$xB = (1/c)$$\partial$$E/$$\partial$$t) after a spatial reflection it would be "left handed," ($$\nabla$$xB = (-1/c)$$\partial$$E/$$\partial$$t) which does not exist in the real world, which therefore means that electromagnetism is not invariant over spatial reflections.