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We discuss how massless particle reactions may be incorporated into standard S-matrix theory. The crucial element for doing so is a low energy zero. Examples of reactions where such zeros occur are weak interaction processes involving neutrinos, chirally symmetric massless pion scattering and two photon exchange between neutral systems. These zeros make two body unitarity a good approximation for sufficiently low energy despite the coalescence of multiparticle thresholds. Through two body unitarity, these zeros produce lines of zeros in the absorptive parts and double spectral functions. These lines of zeros are the S-matrix analog of the requirement of an infrared finite field theory. Not only do they produce finite total cross sections at finite energies, but they also allow both upper and lower bounds to be derived for these cross sections at high energies. This upper bound is our main result. If a plausible smoothness assumption is made, we find oror < fl (where B is arbitrarily small). In particular, the experimentally observed linear rise of the neutrino proton cross section cannot continue indefinitely.
๐ SIMILAR VOLUMES
An asymptotic method of analysis of fluctuations in systems far from equilibrium is developed. A systematic singular perturbative expansion of the equation for the generating function is set up, using as smallness parameter the inverse of the size of the system. Static and time-dependent properties
Faddeev's Hamiltonian path integral method for singular Lagrangians is generalized to the case when second-class constraints appear in the theory. The general formalism is then applied to several problems: quantization of the massive Yang-Mills field theory, light-cone quantization of the self-inter