Lagrangian formalism of polymer theory

In order lo study the properties of polymer solutions, des (. loizeaux (1975) writes the action in the absence of the field A[ 1 ] as 

After the mass renormalization in a space with d 4, the short-range interaction potential is assuin d lo be 

Functions 10 can be expanded into a Taylor series in terms of the interaction parameter. If one employs the following expression for the frc propagator 

a factor (k associated with each part of the solid line  

a factor Vis associated with each dashed line  

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