Quantizing field theories in noncommutative geometry and the correspondence between anti de Sitter space and conformal field theory

Abstract By using the approach of non-commutative geometry, we study spinors and scalars on the two layers AdS d +1 space. We have found that in the boundary of two layers AdS d +1 space, by using the AdS/CFT correspondence, we have a logarithmic conformal field theory. This observation propose a way to get the quantum field theory in the context of non-commutative geometry.