The name is absent

by

J^<7(^r,s; [w]) = ^∙V²g(r,s; [w]) - w(γ)q(γ,s; [w]),            (8.22)

with the initial condition, <γ(r, 0; [w]) = 1. The average segment density of the single
chain in presence of the external field is given by

ʃ Drp(r) exp (—Z3t7₀[r] - βUι[r, w])
ʃ Drexp (-βU₀[r] - ∕3Dι[r,w])

1

VQ[w]

We can also derive the density of the segment located at the contour position, s,

^ɪɪ^(r, N-s- [w])₉(r, s- [w]).

These results (eqs. 8.20 and 8.23) are for linear homopolymers. The derivation can
be generalized to a variety of chain structures, as shown in detail in ref. [269].

8.2 From particles to fields

The preliminary step in a field-based approach, such as SCFT, is to convert the
standard particle-based model to a statistical field theory. This particle-to-field trans-
formation technique for a homopolymer in an explicit solvent is discussed here in
detail. The intramolecular long-range interferences and inter-molecular interactions
between the segments of the polymer chains as well as the interactions with the sol-
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