The 4PI Effective Action for φ^4 Theory

Details The 4PI Effective Action for φ^4 Theory The 4PI Effective Action for φ^4 Theory

2004-01-16

arxiv.org/abs/hep-ph/0401123v1

Eur.Phys.J. C35 (2004) 383-392

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 pages

Scientific paper

We work with $\phi^4$ 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 $n$PI effective action.

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