Abstract
An expansion of the type is derived, where are labels for infinite-dimensional symmetric tensor representations of the Euclidean conformal group ,, the constants are real, and and have the properties of vacuum expectation values of field products. The starting point is an infinite set of coupled nonlinear integral equations for Euclidean Green's functions in space-time dimensions of the type written some 15 years ago by Fradkin and Symanzik. The Green's functions of the corresponding Gell-Mann-Low limit theory are expanded in conformal partial waves. The dynamical equations imply the existence of poles and factorization of residues in the partial waves as functions of the representation parameters. In proving the validity of the expansion we use some differential relations between partially equivalent exceptional representations of , established in an earlier paper. This work completes the group-theoretical derivation of the vacuum operator-product expansion undertaken by Mack in 1973.
- Received 13 August 1975
DOI:https://doi.org/10.1103/PhysRevD.13.887
©1976 American Physical Society