Continuous chain model a fundamental identity

We consider N chains of areas S(,.. ., SN in a d-dimensional continuous space. Each chain j (where y = 1,.. ., /V) is characterized by a function ry(sy) where 

RELATIONS BETWEEN CHAIN THEORY AND FIELD THEORY 

The interaction energy can be expressed in terms of the area concentration 

Let us now introduce an inhomogeneous source J(r) coupled to the concentration ( ). (This reminds us of Edwards s transformation provided we put J — — i% see Chapter 10, Section 3.) Setting 

we remark that any functional of ( ) can be written in the (symbolic) form 

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