Abstract
It has been noted that Bose-Einstein statistics of a scalar field follows from gravitationally induced particle creation. We point out that Fermi-Dirac statistics is allowed when there are two or more scalar fields obeying the same field equation. We determine the general form of allowed anticommutation relations and find that the anticommutation relations satisfied by Faddeev-Popov ghosts fit into this form and, therefore, that they are consistent with particle creation caused by a gravitational background. A similar result is obtained for allowed (bosonic) commutation relations of spinor fields. These opposite spin-statistics relations require negative-norm states.
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