https://doi.org/10.1140/epjc/s2004-01849-6
theoretical physics
The 4PI effective action for 
theory
1
Department of Physics, Brandon University, R7A 6A9, Brandon, Manitoba, Canada
2
Winnipeg Institute for Theoretical Physics, Winnipeg, Manitoba, Canada
* e-mail: carrington@brandonu.ca
Received:
11
March
2004
Published online: 26 May 2004
We work with theory and study the 4PI effective action at 3-loop order. We discuss the relation 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 connected 2-point function is identical to the SD equation for the truncated 2-point function; differentiating with respect to the connected 3-point function reproduces the SD equation for the truncated 3-point function, up to 1-loop order; and differentiating with respect to the connected 4-point function reproduces the SD equation for the truncated 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.
© Springer-Verlag, 2004
