Multilegged propagators in strong-coupling expansions

This paper is a continuation of a previous paper on strong-coupling expansions in quantum field theory. We are concerned here with one-dimensional quantum field theories (quantum-mechanical models). Our general approach is to derive graphical rules for constructing the strong-coupling expansion from a Lagrangian path integral in the presence of external sources. After reviewing the normalization of one-dimensional path integrals, we examine in detail the model Hamiltonian $H=\left|p\right|+\left|q\right|\mathrm{}$. We show that in the strongcoupling expansion the graphs are constructed from multilegged propagators attached to multilegged vertices. We use these graphical rules to calculate the ground-state energy for this Hamiltonian. One motivation for examining expansions involving multilegged propagators is provided by the Lagrangian for quantum chromodynamics whose strong-coupling expansion also involves multilegged propagators.