Application of the N-Quantum Approach to a Renormalizable Field Theory

The N-Quantum Approximation (NQA) is applied to a simple renormalizable field theory, lambda phi^4. Inclusion of the one-loop renormalization of this theory into the NQA approach is demonstrated. Use is made of this one-loop renormalization in a discussion of scattering and the two-body bound state mass. In particular, the function which in the NQA approach plays the role of 2-to-2 scattering amplitude is derived non-perturbatively in a large N limit. The mass of the two-body bound state is also derived two ways in this limit; from an eigenvalue condition for the two-body bound state wave function and also from the timelike zeroes of the 2-to-2 scattering amplitude. Our results, using the NQA, agree with previous calculations using other non-perturbative methods. A discussion of spontaneous symmetry breaking (SSB) from the NQA point of view is also given. Equations governing SSB in lambdaphi^4 are derived in a manner easily generalizable to other theories. These equations are used to derive the famous result on one-loop radiatively induced SSB due to Coleman and Weinberg. Our calculation is conceptually simple and leads naturally to the evaluation of only a single diagram.