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By Eric Harold Neville
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Historically1 the preceding interpretation of Maxwell 1s equations is due to Hermann Weyl 1 in an attempt to combine Einstein 1S general relativity theory and electromagnetism into a single field theory. His idea was that general relativity is naturally expressed in this framework through a structure group 0(4) whereas an electromagnetic field Ieads to an additional scale factor so that the combined structure group is 0(4) X IR. e. matter determines how a vector is rotated under parallel transport 1 whereas in the absence ofmatter 1 one gets an abelian theory1 and charge determines how a vector is changed in length when transported around a curve 1 precisely as described above in the abelian case of gauge theory.
Matter determines how a vector is rotated under parallel transport 1 whereas in the absence ofmatter 1 one gets an abelian theory1 and charge determines how a vector is changed in length when transported around a curve 1 precisely as described above in the abelian case of gauge theory. This idea of change of scale 1 however 1 was rejected on physical grounds by Einstein 1 because if a clock 1 transported around a closed loop 1 would change its scale 1 it would also measure time differently1 and hence the physics of a particle would depend on its history.
31) s = eiu, with real valued u, hence s· (A) a + i du, so that the group of gauge transformations only introduces a phase factor) In any case, Hodge theory, where one seeks a harmonic form representing a given coho- mology dass, represents a linear model for the nonlinear Yang-Mills problem. 1 that introduces some ideas that will also be useful for the nonlinear analysis. In electromagnetic theory, one has a Lorentz manifold M instead of a Riemannian manifold but our formalism applies in the same way.