Conformal 3-Point Functions and the Lorentzian OPE in Momentum Space

Marc Gillioz
SPRINGER, 2020
Journal paper

In conformal field theory in Minkowski momentum space, the 3-point correlation functions of local operators are completely fixed by symmetry. Using Ward identities together with the existence of a Lorentzian operator product expansion (OPE), we show that the Wightman function of three scalar operators is a double hypergeometric series of the Appell F-4 type. We extend this simple closed-form expression to the case of two scalar operators and one traceless symmetric tensor with arbitrary spin. Time-ordered and partially-time-ordered products are constructed in a similar fashion and their relation with the Wightman function is discussed.

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Marc Gillioz
SPRINGER, 2020
Journal paper

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https://infoscience.epfl.ch/record/279843?ln=en

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Minkowski space

In mathematical physics, Minkowski space (or Minkowski spacetime) (mɪŋˈkɔːfski,_-ˈkɒf-) combines inertial space and time manifolds (x,y) with a non-inertial reference frame of space and time (x',t')

Conformal field theory

A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformati

Position and momentum spaces

In physics and geometry, there are two closely related vector spaces, usually three-dimensional but in general of any finite dimension. Position space (also real space or coordinate space) is the se