Correspondence with a set of fields

Let us consider N free fields (f j(j = 1. IV), each of them with n components Pj, 1 = 1. n) taking values py,(r) at each point r. We can write these functions in the form py,(r) = (r py,), by considering them as the components of a vector py,) which is real. 

Let us associate the following weights with the configurations of the system °ir = exp[ - 

RELATIONS BETWEEN CHAIN THEORY AND FIELD THEORY 

By bringing this result in (11.4.10) and by remarking that the fields are independent of one another, we obtain 

The theory is defined for integer-values of n however, it can be extended to all values of n by analytic continuation. Thus, in the limit n - 0, we find 

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