1206.0239 (Karen Yagdjian)

Huygens' Principle for the Klein-Gordon equation in the de Sitter
spacetime    [PDF]

Karen Yagdjian

In this article we prove that the Klein-Gordon equation in the de Sitter spacetime obeys the Huygens' principle if and only if the physical mass $m$ of the scalar field and the dimension $n$ of the spatial variable are tied by equation $m^2=(n^2-1)/4 $. Moreover, we define the incomplete Huygens' principle, which is the Huygens' principle restricted to the vanishing second initial datum, and then reveal that the massless scalar field in the de Sitter spacetime obeys the incomplete Huygens' principle for the dimensions $n=1,3$, only. In fact, for $n=3$ these two values of the mass are the endpoints of the so-called in quantum field theory the Higuchi bound. The value $m^2=(n^2-1)/4 $ of the physical mass allows us also to obtain complete asymptotic expansion of the solution for the large time.

View original: http://arxiv.org/abs/1206.0239