Green's Theorem and Invariant Transformations

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Abstract
Conservation laws are derived with the use of Green's theorem. These are studied specifically for the wave equation. A trivial class of invariant transformations exists which maps solutions into solutions. The mapping consists in the addition of a particular solution to all solutions. Because of the linearity of the wave equation, this sum will again be a solution. It is shown that this class of transformations has the Newman-Penrose constants among its generators. Calculations are carried out explicitly for the scalar wave equation and for Maxwell's equations.

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