Example of the Antisymmetry Laws

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In electrodynamics, the antisymmetry laws immediately refute U(1) sector symmetry and immediately refute gauge freedom. In the old U(1) gauge theory, a commutator of covariant derivatives acted on a gauge field. For example, in L. H. Ryder’s book, “Quantum Field Theory” (Cambridge, 1996, 2nd. ed.) this method is described in his eqs. (3.165) ff. and is now thoroughly obsolete as explained in the set of notes 131 and 132 for example. The B(3) field observed experimentally in the inverse Faraday effect assumes ever more fundamental importance as the old theory of electrodynamics collapses entirely. Everything in electrodynamics is now described directly by the spin connections, not by the old Heaviside potentials of the nineteenth century. The antisymmetry laws are obvious (in retrospect as usual) and were missed out of habit, i.e. out of routine acceptance. This is the usual thing in science. One uses something for many years and suddenly realizes that it is incomplete or plain wrong. Gauge freedom in classical electrodynamics was always unsatisfactory, and has now been removed completely. This process started in ECE theory in paper 71, and the antisymmetry laws spectacularly confirm that gauge freedom is meaningless. General relativiy is a natural and powerful theory which should replace gauge theory and the Higgs mechanism in field / particle theory.

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