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D (k)! @ ? @ k 2 3! @ ? @ ? @ O(k) terms in the density}density correlator. 35) when one variation acts on the ) part of the h interaction in Eq. 32) and the other variation acts on the classical interaction. 52), which illuminates the character of the theory, is as ? follows. e c be maintained, implying that this "eld and ? ? the chemical potentials always appear in the combination #ie . This requirement casts the theory in its most useful ? form. However, since is simply a dummy integration variable, one is free to make "eld rede"nitions that violate this restriction, and it is sometimes convenient to do so temporarily.

118) in Eq. @ e CI (k) e . 122) 3. E4ective 5eld theory We have just worked out the statistical mechanics of a classical, multicomponent plasma through one-loop order. One cannot go to higher order in this purely classical theory. Ultraviolet divergences appear at two-loop order and beyond. 1) which is proportional to the integral of the cube of the Debye Green's function, (dJr)G (r). In J three dimensions, the short-distance part of this integral behaves as (dr)/r, which is logarithmically divergent.

As in the original ? classical theory. Rather, 1n 2 , ? @ ln Z "! S " ne @C? (! S ? @ " ln Z (r) (r) ? @ S S (r) (r) ? @ ? 1n 2 1n 2 ! @ @ @ , ? 34) S (r) @ (r) . 4. Renormalization The residue of a pole in an induced coupling may be determined by calculating a suitable n-point density correlator to a given loop order, and requiring that the result be "nite as P3. Once this has been done for all the couplings that appear in a given order, then any other process will be "nite to this order.

### Physics Reports vol.340

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