Harmonic bilocal fields generated by globally conformal invariant scalar fields

Details Harmonic bilocal fields generated by globally conformal invariant scalar fields Harmonic bilocal fields generated by globally conformal invariant scalar fields

2007-04-16

arxiv.org/abs/0704.1960v4

Commun.Math.Phys.279:225-250,2008

Physics

High Energy Physics

High Energy Physics - Theory

29 pages. v2: corrected an argument, v4: final version as to be published in CMP

Scientific paper

10.1007/s00220-007-0394-0

The twist two contribution in the operator product expansion of phi_1(x_1) phi_2(x_2) for a pair of globally conformal invariant, scalar fields of equal scaling dimension d in four space-time dimensions is a field V_1(x_1,x_2) which is harmonic in both variables. It is demonstrated that the Huygens bilocality of V_1 can be equivalently characterized by a "single-pole property" concerning the pole structure of the (rational) correlation functions involving the product phi_1(x_1) phi_2(x_2). This property is established for the dimension d=2 of phi_1, phi_2. As an application we prove that any system of GCI scalar fields of conformal dimension 2 (in four space-time dimensions) can be presented as a (possibly infinite) superposition of products of free massless fields.

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