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Green's Theorem and Invariant Transformations

### 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.

© 1968 The American Institute of Physics

Received 06 October 1967
Published online 28 October 2003

/content/aip/journal/jmp/9/5/10.1063/1.1664627

http://aip.metastore.ingenta.com/content/aip/journal/jmp/9/5/10.1063/1.1664627

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