Lectures on the Mandelstam Representation [MatSciRep:6]

Abstract

Part I : For Strong interaction scattering processes, an abstract approach (theory with no infinities) based on the general principles like Lorentz invariance, causality and unitary deduced from field theories is utilized and the mathematical implications are studied. It is to prove dispersion relations by establishing analyticity properties of matrix elements. A representation for arbitrary energy and momentum transfer has been given by Mandelstam using the theory of two complex variables. Part II: Titchmarsh Theorem could be used, where under certain restrictions the real and imaginary parts of the Fourier transform of a function which vanishes for negative values of the argument are Hilbert transforms of each other.