Complex Angular Momentum Diagonalization of the Bethe-Salpeter Structure in General Quantum Field Theory
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The Complex Angular Momentum (CAM) representation of (scalar) fourpoint 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 λt, 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.
KeywordsQuantum Field Theory Asymptotic Behaviour General Principle Spectral Property Regge Pole
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