Classical Field Theory and Gravitation in a de Sitter World

The algebra and the calculus pertaining to a certain class of representations of the de Sitter group is developed. This permits us to formulate covariant field equations in de Sitter space, and, in particular, to construct quantum mechanical equations of motion associated with particles of given spin. The gauge principle is invoked and a spin-two field emerges, which we identify with the gravitational field. Its coupling to sources is discussed and conservation laws are derived. The emerging nongeometric theory of gravitation is compared with both the Einstein-Riemann type and other previously proposed nongeometrical theories.