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Theoretical and Mathematical Physics

, Volume 135, Issue 1, pp 520–530 | Cite as

Wave Equations in Riemannian Spaces

  • X. S. Mamaeva
  • N. N. Trunov
Article

Abstract

With regard to applications in quantum theory, we consider the classical wave equation involving the scalar curvature with an arbitrary coefficient ξ. 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 ξ. These properties depend essentially not only on the values of ξ 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 ξ. The same value of ξ follows from other arguments and the relation to the known WKB transformation method that we establish.

wave equation curved space–time conformal invariance conformal transformation Huygens principle 

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • X. S. Mamaeva
    • 1
  • N. N. Trunov
    • 2
  1. 1.St. Petersburg University of Economics and FinanceSt. PetersburgRussia
  2. 2.Mendeleev All-Russian Research Institute for MetrologySt. PetersburgRussia

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