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Cauchy’s problem and Huygens’ principle for relativistic higher spin wave equations in an arbitrary curved space-time. (English) Zbl 0564.35091
Relativistic spin s(s\(\geq 1/2)\), nonzero mass equations are given which in an arbitrary curved space-time are internally consistent. By means of Riesz’ integration method a representation theorem for the solution of Cauchy’s problem, using the constraints of the Cauchy data on the initial hypersurface and suitable ”Green’s formulas,” is proved. Finally, a necessary and sufficient condition for the validity of Huygens’ principle is stated from which it follows that only in space-times of constant curvature do the field equations satisfy Huygens’ principle.

35Q99 Partial differential equations of mathematical physics and other areas of application
35C15 Integral representations of solutions to PDEs
83C15 Exact solutions to problems in general relativity and gravitational theory
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