The significance of conformal inversion in quantum field theory

The 2-point functions of Euclidean conformal invariant quantum field theory are looked at as intertwining kernels of the conformal group. In this analysis a fundamental role is played by a two-element groupW, whose non-identity element =R·I consists of the conformal inversionR multiplied by a space-time reflectionI. The propagators of conformal invariant quantum field theory are determined by the requirement of -covariance. The importance of the -inversion in the theory of Zeta-functions is mentioned.