Krein space quantization of linear gravity in de Sitter spacetime and generalization to QFT

It has been shown that the negative-norm states or negative-frequency solutions of the field equation are indispensable for a fully covariant quantization (Krein space quantization) of the minimally coupled free scalar field in de Sitter spacetime. The new method of quantization has been applied for the free boson and spinor fields in Minkowski spacetime, and the basic structure of quantum field theory is reformulated in Krein space. It is seen that the presence of unphysical negative-frequency states plays the role of an automatic renormalization tool for the theory.