Fwd: Example of the New Symmetry Relations of Electrodynamics

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Subject: Example of the New Symmetry Relations of Electrodynamics
Date: Thu, 9 Apr 2009 05:30:05 EDT


Attachment: anexamplefromatkins.pdf

On the U(1) level of electrodynamics (Maxwell Heaviside electrodynamics) the newly discovered symmetry relations are:

partial sub mu A sub nu = – partial sub nu A sub mu

My sometime Oxford colleague Peter Atkins gives an example in his eq. (14.2.7), page 382 of the second edition of his multi edition, “Molecular Quantum Mechanics”, (OUP, 1983, softback). This is one of his hugely successful books. They are successful because the give a lot of clear detail. This book has its own problem solver book. In Atkins’ equation:

partial A sub X / partial Y = – partial A sub Y / partial X

which is antisymmetric QED. On the O(3) and ECE levels of electrodynamics this antisymmetry works its way into the definition of the B(3) field via the commutator of complex valued potentials as follows:

B(3)* = – i g A(1) x A(2) = i g A(2) x A(1),

QED.

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