Rigorous Methods in Particle Physics

The book addresses three major topics in mathematical physics: 1. recent rigorous results in potential theory with appli- cations in particle physics, 2. analyticity in quantum field theory and its applica- tions, and 3. fundamentals and applications of the inverse problem. In addition, the book contains some contributions on questions of general interest in quantum field theory such as nonperturbative solutions of quantum chromodynamics, bifurcation theory applied to chiral symmetry, as well as exactly soluable models. The volume closes with a brief review of geometric approaches to particle physics and a phenomenological discussion of Higgs interactions.

A model for a dia-electric.- Potential models for quarkonium systems.- Some new bounds on the number of bound states.- Moment inequalities and a Martin conjecture.- On a class of spectral problems admitting partial algebraization.- High energy theorems.- Complex angular momentum analysis in axiomatic quantum field theory.- Inverse scattering revisited: Explicit solution of the Marchenko-Martin method.- The inverse of an inverse problem.- Weak-star compactness and its relevance to analyticity problems.- Variational improvement of perturbation theory and/or perturbative improvement of variational calculations.- A new method for QCD sum rules: The L? norm approach.- Bifurcation theory applied to chiral symmetry breaking.- On the scaling behavior of the O(N) ?-model.- A conjecture on the possible exact (1+1)-dimensional solutions to the discrete Boltzmann models I.- Are heavy Higgs interactions observable at the 100 GeV scale?.- Geometric approaches to particle physics.