Greens functions and diagrams

2 Description of the Landau-Ginzburg model 5.2.1 Green s functions and diagrams 

With each space point r, let us associate the tt components (pj(r) of a random field j . The weight corresponding to a configuration of the field is [see (11.4.32) and (11.4.33)] 

A short-distance cut-off is also introduced in order to ensure convergence. In polymer theory, we are interested in the limit n - 0, but here we assume that n is a positive integer. 

The index G indicates that here we are dealing with general Green s functions 

The generating function of the Green s functions is by definition a functional of an auxiliary field with n components Bj(r) 

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