2004/01/16 by M. E. Carrington
Physics and Astronomy · #hep-ph
published as Eur.Phys.J. C35 (2004) 383-392 · 13 pages
arxiv created 2004/01/16 · arxiv updated 2009/12/01
We work with ϕ4 theory and study the 4PI effective action at 3-loop order. We discuss the relationship between the equations of motion obtained by taking functional derivatives of the effective action with respect to the variational parameters, and the Schwinger-Dyson (SD) equations. We show that the equation obtained by differentiating with respect to the 2-point function is identical to the SD equation for the 2-point function; differentiating with respect to the 3-point function reproduces the SD equation for the 3-point function, up to 1-loop order; and differentiating with respect to the 4-point function reproduces the SD equation for the 4-point function, at the tree level. These results establish a connection between two techniques for performing non-equilibrium calculations, and provide a starting place for a study of the gauge dependence of quantities derived from an nPI effective action.