Renormalization fully renormalized kinetic theory

It should be noted that the integrodifferential equations equivalent to Eqs. (3.168) were first obtained with the fully renormalized kinetic theory of Yang, Lee, and Shin (YLS) [132]. However, they had not confined themselves to the original integral equations (3.168) but reduced them to the differential rate equations by the incorrect substitution used instead of (3.164) ... 

The main objective of our theory is to develop useful methods for approximating the memory function. Two basic motivations characterize our analysis in Section 3, the systematic inclusion of the exact correlation functions and the expression of the memory function in terms of an effective two-body problem, which constitutes a second renormalization. The second motivation is particularly important in setting up approximation schemes since we are conditioned to think in terms of two-body collision processes. In Section 4 we use these ideas to arrive at an approximate expression for the memory function. The memory function is the sum of a Boltzmann-Enskog term and a recollision term that describes the correlated dynamical processes mentioned above. We will call this theory the fully renormalized kinetic theory because the medium effects involving particles other than the interacting binary cluster are taken into account and also because bare interactions are replaced by effective interactions, which depend on the equilibrium correlations in the fluid. 

In the formalism of fully renormalized kinetic theory (FRKT) one directs one s attention not to the phase space correlation function 0(12) but to the associated memory function < (12), which is defined by " ... 

However, MET is not a unique theory accounting for the higher-order concentration corrections. Similar results were obtained within the fully renormalized YLS (Yang-Lee-Shin) theory [132], which is also integrodiffer-ential and employs the kernels containing concentration corrections as compared to those in IET. It was shown in Ref. 41 that both these theories, MET and YLS, provide the correct asymptotic expressions for binary kinetics, but differ slightly in the nonlinear terms of the concentration expansion. There were also a number of other attempts to overcome the concentration limitations of the theory made by the same Korean group earlier (in superposition approximation [139,141,142]) and later [numerous multiparticle kernel (MPK) theories [51,126]]. 

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