Local field factors potentials

N. The N dependence of fis/N 0.15 has previously been found [145] for the same potential and the polyene alternations 8 = 0.07. The measured [111]/values for the 0-0 line of PDA crystals in Fig. 6.14 are around 0.6 per repeat unit, or 0.15 per tt electron. The 0-0 line is several times more intense at 10 K than the O-I sidebands. The total oscillator strength of the exciton is /ib 0.7-0.8 per repeat unit, or 0.18-0.20 per 8 electron, slightly above the PPP estimate. As there are no adjustable parameters or scale factors, oligomers with molecular V(R) account directly for the polymer intensity. Local field and other corrections will be needed for more stringent comparison. 

Similar analysis can be made for other types of materials. Thus, as a generalization, the curvature of a surface causes field intensification, which results in a higher current than that on a flat surface. Although the detailed current flow mechanism can be different for different types of materials under different potentials and illumination conditions, the effect of surface curvature on the field intensification at local areas is the same. The important point is that the order of magnitude for the radius of curvature that can cause a significant effect on field intensification is different for the substrates of different widths of the space charge layer. This is a principle factor that determines the dimensions of the pores. 

Gauge fields (M) that restore local phase invariance are evidently closely related also to the quantum-potential field. The wave function of a free electron, with temporal and spatial aspects of the phase factor separated, may be written as... 

Since ip depends on space-time coordinates, the relative phase factor of ip at two different points would be completely arbitrary and accordingly, a must also be a function of space-time. To preserve invariance it is necessary to compensate the variation of the phase a (a ) by introducing the electromagnetic potentials (T4.5). In similar vein the gravitational field appears as the compensating gauge field under Lorentz invariant local isotopic gauge transformation [150]. 

Chemical behaviour depends on chemical potential and electromagnetic interaction. Both of these factors depend on the local curvature of space-time, commonly identified with the vacuum. Any chemical or phase transformation is caused by an interaction that changes the symmetry of the gauge field. It is convenient to describe such events in terms of a Lagrangian density which is invariant under gauge transformation and reveals the details of the interaction as a function of the symmetry. The chemically important examples of crystal nucleation and the generation of entropy by time flow will be discussed next. The important conclusion is that in all cases, the gauge field arises from a symmetry of space-time and the nature of chemical matter and interaction reduces to a function of space-time structure. 

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