标题： 由全局共形不变标量场生成的调和双局域场 显示英文标题

标题： Harmonic bilocal fields generated by globally conformal invariant scalar fields

摘要： 在四维时空下，对于一对具有相同标度维度d的全局共形不变标量场φ₁(x₁)和φ₂(x₂)的算符乘积展开中，自旋二贡献是一个双变量都具有调和性的场V₁(x₁,x₂)。 证明了V₁的胡克司双局域性可以通过涉及φ₁(x₁)φ₂(x₂)乘积的（有理）相关函数的“单极性质”来等价刻画。 这一性质被确立在φ₁、φ₂的标度维度d=2的情况下。 作为一个应用，我们证明了任何具有共形维度2（在四维时空下）的GCI标量场系统都可以表示为自由无质量场乘积的（可能是无限的）叠加。 显示英文摘要

摘要： 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.