Operator product expansions on the vacuum in conformal quantum field theory in two spacetime dimensions

Let phi1(x) and phi2(y) be two local fields in a conformal quantum field theory (CQFT) in two-dimensional spacetime. It is then shown that the vector-valued distribution phi1(x) phi2(y) /0 > is a boundary value of a vector-valued holomorphic function which is defined on a large conformally invariant domain. By group theoretical arguments alone it is proved that phi1(x) phi2(y) /0 > can be expanded into conformal partial waves. These have all the properties of a global version of Wilson's operator product expansions when applied to the vacuum state /0 >. Finally, the corresponding calculations are carried out more explicitly in the Thirring model. Here, a complete set of local conformally covariant fields is found, which is closed under vacuum expansion of any two of its elements (a vacuum expansion is an operator product expansion applied to the vacuum). (orig.)