Dynamical derivation of vacuum operator-product expansion in Euclidean conformal quatum field theory
An expansion of the type < phi (x$sub 1$)...phi (x/subn/) > $sub 0$ = < phi (x$sub 1$) phi (x$sub 2$) > $sub 0$ < phi (x$sub 3$)...phi (x/subn/) > $sub 0$ + $Sigma$/sub chi/l C$sup 2$(chi/subl/) $Integral$ (dp) Q/sup chi/l (x$sub 1$,x$sub 2$;-p) w/sub chi/l(p) Q/sup chi//subl/(p;x$sub 3$,... x/subn/) is derived, where chi/subl/ = l,c/subl/ are labels for infinite-dimensional symmetric tensor representations of the Euclidean conformal group O/sup arrow-up/ (2h + 1, 1), X$sub 1$ = 1, -c/subl/, the constants C (x/subl/) are real, and Q/ sup chi/ and w/sub chi/ 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 2h 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, use is made of some differential relations between partially equivalent exceptional representations O/sup arrow-up/(2h + 1, 1), established in an earlier paper. This work completes the group-theoretical derivation of the vacuum operator-product expansion undertaken by Mack in 1973. (AIP)
- Research Organization:
- Joseph Henry Laboratories of Physics, Princeton University, New Jersey 08540
- NSA Number:
- NSA-33-032080
- OSTI ID:
- 4007884
- Journal Information:
- Phys. Rev., D, v. 13, no. 4, pp. 887-912, Other Information: Orig. Receipt Date: 30-JUN-76
- Country of Publication:
- United States
- Language:
- English
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