Light cone expansion and four point function

The behaviour of products of local fields for lightlike distances is investigated. If a light cone expansion ofA(x)A(y) exists, then already the four point function carries the singularity arising in the expansion for (x–y)²0. For a special class of field theories, discussed by S. Schlieder and E. Seiler, it is shown that the light cone expansion is possible. Notation. the Schwartz space of strongly decreasing testfunctions over ⁿ A=scalar field operator, which fulfils the Wightman axioms we freely writeA(x),x ⁴ andA(g),g ]. =Hilbert space. =vacuum state. is the linear hull of the vectors (With respect to the definition of operators with complex argument cf.6]!) By (x ²) (x ²) we denote a sequence of functions which converges to (x ²) as 0.