Wave Equations in the de Sitter Space

Details Wave Equations in the de Sitter Space Wave Equations in the de Sitter Space

Jul 1949

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1949phrv...76..296w&link_type=abstract

Physical Review, vol. 76, Issue 2, pp. 296-297

Physics

4

Scientific paper

The second-order wave equation ∂2u∂xi∂xi=0 in five-dimensional flat space can reproduce approximately the field hitherto considered in four-dimensional space, if a de Sitter space with the radius R is imbedded in the five-dimensional flat space and the derivative of the wave function u in the direction normal to this de Sitter space is assumed to be equal to imu, where m is a constant proper to the field. Conversely, the ordinary field equations in four-dimensional space can be regarded as valid only for a portion of de Sitter space with the linear dimension, which is small compared with the radius R of the universe. Extensions of these arguments to electromagnetic field and spinor field are also considered.

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