Abstract
It is proven that for each given two-field channel — called the “t-channel”— with (off-shell) “scattering angle”\(\Theta_t\), the four-point Green's function of any scalar Quantum Fields satisfying the basic principles of locality, spectral condition together with temperateness admits a Laplace-type transform in the corresponding complex angular momentum variable \(\lambda_t\), dual to \(\Theta_t\). This transform enjoys the following properties: a) it is holomorphic in a half-plane of the form Re\(\lambda_t\) >m, where m is a certain “degree of temperateness” of the fields considered, b) it is in one-to-one (invertible) correspondence with the (off-shell) “absorptive parts” in the crossed two-field channels, c) it extrapolates in a canonical way to complex values of the angular momentum the coefficients of the (off-shell) t-channel partial-wave expansion of the Euclidean four-point function of the fields. These properties are established for all space-time dimensions d + 1 with d≥ 2.
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