  The Complex Angular Momentum (CAM) representation of (scalar) four-point
functions has been previously established starting from the general principles
of local relativistic Quantum Field Theory (QFT). Here, we carry out the
diagonalization of the general $t$-channel Bethe--Salpeter (BS) structure of
four point functions in the corresponding CAM variable $\lambda_{t},$ for all
negative values of the squared-energy variable $t$. This diagonalization is
closely related to the existence of BS-equations for the absorptive parts in
the crossed channels, interpreted as convolution equations with spectral
properties. The production of Regge poles equipped with factorized residues
involving Euclidean three-point functions appears as conceptually built-in in
the analytic axiomatic framework of QFT. The existence of leading Reggeon terms
governing the asymptotic behaviour of the four-point function at fixed $t$ is
strictly conditioned by the asymptotic behaviour of a global Bethe-Salpeter
kernel of the theory.
