Wightman Formulation for the Quantization of the Gravitational Field

Abstract

A generalization of Wightman field theory is formulated which makes the theory also applicable to the gravitational field. Strongly geodesically complete manifolds are found to be the most suitable for description of curved space-time in our approach. After the formulation of generalized axioms, the schemes of proofs of the fundamental theorems of the theory (Bargmann-Hall-Wightman theorem, $\ensuremath{\theta}$ theorem, main reconstruction theorem, etc.) are given. The paper ends with hints on the possible ways of constructing the theory of asymptotic states for the quantized gravitational field.