Arbitrariness of the General Solution and Symmetries
Reference: Acta Applicandae Mathematicae, 41 (1995) 311-322
Description: Here I applied some of the results obtained in [5] to problems related to symmetries. It is well-known that Lie theory allows us to find only special solutions of a system of PDEs. I was interested in determining how special these solutions are, i.e. how much of the solution space we miss. Using the method of differential constraints this can be done fairly easily for normal systems. As a second topic I applied the results of [5] on gauge symmetries to the Lorentz gauge in electromagnetism and to harmonic coordinates for the Einstein equations.
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