Spectrum of Hawking radiation and the Huygens principle.

It has been established that the Minkowski vacuum observed by a uniformly accelerating detector can be equivalently described by a canonical ensemble of states. However, recent calculations have revealed that in a spacetime of odd dimensions free massless scalar particles are detected with the Fermi-Dirac distribution instead of the Planck one. The purpose of this paper is to solve this apparent puzzle. It is concluded that the cause of this phenomenon is the lack of the Huygens principle in odd dimensions: the expectation value of the commutator of massless fields does not vanish in the timelike region. The case of a spinor field is treated equally. Other spacetimes, de Sitter space and Schwarzschild space, are also discussed.