Geodesic
Wave Equations in Riemannian Spaces
Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 1, pp. 82-94

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With regard to applications in quantum theory, we consider the classical wave equation involving the scalar curvature with an arbitrary coefficient $\xi$. General properties of this equation and its solutions are studied based on modern results in group analysis with the aim to fix a physically justified value of $\xi$. These properties depend essentially not only on the values of $\xi$ and the mass parameter but also on the type and dimension of the space. Form invariance and conformal invariance must be distinguished in general. A class of Lorentz spaces in which the massless equation satisfies the Huygens principle and its Green's function is free of a logarithmic singularity exists only for the conformal value of $\xi$. The same value of $\xi$ follows from other arguments and the relation to the known WKB transformation method that we establish.
Keywords: wave equation, curved space-time, Huygens principle.
Mots-clés : conformal invariance, conformal transformation 
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     author = {K. S. Mamaeva and N. N. Trunov},
     title = {Wave {Equations} in {Riemannian} {Spaces}},
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K. S. Mamaeva; N. N. Trunov. Wave Equations in Riemannian Spaces. Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 1, pp. 82-94. http://geodesic.mathdoc.fr/item/TMF_2003_135_1_a3/