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

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SUMMARY

The discussion focuses on the Hamiltonian applicable to a wire coil under reflection transformation, specifically in the context of Noether's theorem. It establishes that electromagnetism is not invariant under reflection transformations, contrary to the invariance observed in electrodynamics under spatial reflections and time reversal. The conversation highlights the necessity of transforming electromagnetic field components appropriately, noting that the right-handed nature of magnetism changes to left-handed post-reflection, which is not physically realizable.

PREREQUISITES
  • Noether's theorem
  • Electromagnetic field theory
  • Reflection transformations in physics
  • Quantum Electrodynamics (QED)
NEXT STEPS
  • Study the implications of Noether's theorem in classical mechanics
  • Research the properties of electromagnetic fields under various transformations
  • Examine the role of charge conjugation in Quantum Electrodynamics
  • Explore the mathematical framework of Hamiltonian mechanics in electromagnetism
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Physicists, particularly those specializing in theoretical physics, electromagnetism, and quantum mechanics, will benefit from this discussion.

zush
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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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