Hartree approximation in relativistic field theory

Abstract

The large-$N$ limit of $\lambda {\phi }^4$ theory with $\mathrm{O}\mathrm{}\left(N\right)\mathrm{}$ symmetry is derived by functional methods. Since the method does not require the cumbersome, detailed analysis of Feynman graphs, it should make possible the study of more complicated theories in the many-field limit.