ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
We reformulate the theory of simple liquids in a field theoretical way by taking into account the triplet potential wijk, in addition to the external potential ui and the pair potential vij. The innovation here is the inversion method and the on-shell expansion which are the building blocks of a novel use of Legendre transformation developed in field theory. By the inversion method, we renormalize the theory in terms of one-, two-, and three-particle densities, and present a diagrammatic representation for a thermodynamical functional, which is the entropy except for a trivial constant, in terms of renormalized variables. In other words, we present an expression for the entropy in terms of only one-, two-, and three-particle densities: the n-particle density where n≥4 does not appear in the expression. The on-shell condition, which is a starting point of the on-shell expansion, of the thermodynamical functional thus obtained (the entropy) leads to a set of three self-consistent equations for one-, two-, and three-particle densities. Through one of the self-consistent equations, we can systematically improve the Kirkwood's superposition approximation for the three-particle density. The on-shell conditions for other thermodynamical functionals, also obtained in this article, are found to be extentions of various well-known equations in the theory of simple liquids. The formulation presented here is complementary to the conventional re-summation techniques for renormalization of diagrams. In the present formulation, we do not have to care about the topological structure of diagrams, often characterized by the irreducibility of diagrams. Instead, by a perturbative calculation, we can automatically single out the diagrams with the topological structure predicted by the re-summation techniques. © 1998 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.532277
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