SOURCE-FIELD CAUSALITY AND ITS APPLICATION TO CLASSICAL RADIATION THEORY.
Physical and mathematical sciences research papers,
AIR FORCE CAMBRIDGE RESEARCH LABS L G HANSCOM FIELD MASS
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A mathematical procedure is given for singling out the causal solutions from the general set of solutions of self-adjoint differential equations. It consists in splitting the self-adjoint equation into a pair of adjoint equations whose solutions are purely causal and purely anti-causal, respectively. A subsequent merging of the equations then generates in full detail, including singularities, the causal and anti-causal solutions of the original self -adjoint equation. As an important example, it is shown that the dAlembertian with point source has a legitimate causal solution involving both retarded and advanced potentials at the source point itself, while at all other points, the retarded potential alone satisfies causality. Within the context of the formalism some recent attempts at modifying classical radiation theory can now be reassessed and more clearly categorized. In particular, the Dirac and Wheeler-Feynman approaches are examined in this light. Author
- Quantum Theory and Relativity