The name is absent

polymer contacts. The partition function is given by

∙⅛                 Tip n         Tlg n

Z_c(n_s,n_p,V,D =                   y Dr,∏ J *_iexp(-∕3%(r^np'^v]-∕3t^zι[r"^s+"'^,^'J)

j—1         ⅛—1

δ↑Pp + Ps — Po]>

where δ[pp + ps — Po] imposes the local incompressibility constraint. Noting this
constraint, the interaction potential can be re-written as

_z,_t∕₁[_r"s+"rf] ₌ l_t,<,_χps ʃdr(p= - [⅛(r) - ⅛(r)]²).

Using Hubbard-Stratonovich transformation [269] gives

e '^ib'ⁱ = e ×ps(ⁿs+n_pN)∕i Dw^ exp ( / dr[(βp — ps)w- — (Po/Xps)^,u∙'1] ) , (8.30)

and from the definition of dirac delta functional

δ[pp + Ps - Po]= Dw₊ exp

(8.31)

Here, two auxiliary fields, w₊ and w_, have been introduced to decouple the interac-
tions between the solvent molecules and polymer segments. These can be viewed as
fluctuating chemical potential fields. Field w₊ represents the total chemical potential
while w_ represents the exchange chemical potential. Using these transformations,

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