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Partial wave expansion and Wightman positivity in conformal field theory. (English) Zbl 1128.81320

Summary: A new method for computing exact conformal partial wave expansions is developed and applied to approach the problem of Hilbert space (Wightman) positivity in a nonperturbative four-dimensional quantum field theory model. The model is based on the assumption of global conformal invariance on compactified Minkowski space (GCI). Bilocal fields arising in the harmonic decomposition of the operator product expansion (OPE) prove to be a powerful instrument in exploring the field content. In particular, in the theory of a field \(\mathcal L\) of dimension 4 which has the properties of a (gauge invariant) Lagrangian, the scalar field contribution to the 6-point function of the twist 2 bilocal field is analyzed with the aim to separate the free field part from the nontrivial part.

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T05 Axiomatic quantum field theory; operator algebras
81T08 Constructive quantum field theory
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