The Analytic S-Matrix
Cambridge University Press, Apr 30, 2002 - Science - 296 pages
Certain interactions, such as nuclear forces and the forces of 'high-energy' physics, which arise in the theory of elementary particles, cannot be described successfully by quantum field theory. Considerable interest has therefore centred on attempts to formulate interactions between elementary particles in terms of the S-Matrix, an operator introduced by Heisenberg which connects the input and output of a scattering experiment without seeking to give a localized description of the intervening events. In this book four authors, who are together responsible for many of these developments, set out a theory of the S-Matrix starting, as far as possible, from physically plausible assumptions and investigate the mathematical consequences. The least understood of these assumptions is the vital postulate of analyticity; much insight can however be gained into its working by a study of the Feyman integrals and the book describes what is known about their analytic and high energy properties. Originally published in hardback in 1966.
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acnodes analytic continuation analytic function analytic properties angular momentum argument asymptotic behaviour boundary values branch-point coefficient complex conjugate complex singularities complex surface condition consider contour corresponding crossing crunode d-lines defined discontinuity discussion dispersion relation distorted dual diagram energy energy-momentum example external masses factor factorises Feynman diagram Feynman graph Feynman integral fixed four-momenta give given Hence hermitian analyticity infinity integrand interaction internal lines intersection labels Landau curve Landau equations Landshoff leading behaviour leading singularity linear Lorentz lower-order singularities Mandelstam mass shell matrix elements Mellin transform non-singular normal thresholds obtained parameters path perturbation theory physical region physical sheet physical values pinch plane Polkinghorne positive Regge poles result Riemann sheet right-hand side S-matrix S-matrix theory s-plane scattering amplitude second-type second-type singularities singularity surface structure subenergies theorem three-particle transform triangle graph triangle singularity two-particle undistorted hypercontour unitarity equation unstable particle vanish vectors vertex zero