Many-electron effects in polymers are considered, with emphasis on the way electron-electron interactions are reflected in ground-state properties. After a survey of results on graph theory, built up from valence-bond structures, in which the importance of size consistency again emerges, some specific results of ground-state electron pair correlations in polyacetylene and polydiacetylene are considered, motivated by the linear dispersion of the π-electron plasmon, as measured in the optical experiments of Ritsko et al. The way in which such collective excitations can affect ground-state pair correlations is discussed as is the influence of low dimensionality. A brief summary is given of the way in which the energy gap in polyacetylene and polydiacetylene depends on electron-electron repulsion although unlike the plasmon problem where the long-range Coulomb repulsion e 2/ r ij is essential, this problem is usefully tackled using the on-site Hubbard repulsion. Again, there can be no doubt that correlation is important in the ground states of polyacetylene and polydiacetylene. However, recent work on bond-charge repulsion shows that whether correlation enhances or suppresses dimerization depends strongly on the particular thermodynamic state in question: this is illustrated by specific examples relating to the metal-insulator transition in low-dimensional solids. A quite different aspect of many-body phenomena will then be considered, pertaining especially to AC electrical transport in biopolymers. Here, the importance of disorder in the experimental results currently available is stressed. A power law behaviour of the frequency-dependent conductivity, i.e. σ(ω) proportional to ω s, is a characteristic feature at suitably high frequencies. This focusses attention on the power, s, and a brief discussion of simple models shows that, for those considered to date s< 1, with possible values of 1 4 and 1 2 being exhibited. A possible influence of a compensation effect on the high-frequency conductivity is suggested. It is argued, following Kreuzer and March, that this is a many-particle phenomenon ands = 1-( T/T c) for T < T c, where T c is the compensation temperature; a result apparently due to Dyre. The possibility of further experimental and theoretical studies related to the many-body phenomena is referred to.
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