Completeness relations, path-integral

The path L can have an arbitrary shape, and it can intersect media characterized by various physical properties. In particular, it can be completely contained within a conducting medium. Because of the fact that the electromotive force caused by electric charges is zero, a Coulomb force field can cause an electric current by itself. This is the reason why non-Coulomb forces must be considered in order to understand the creation of current flow. Equation 1.46 is the first Maxwell equation for electric fields which do not vary with time, given in its integral form, and relates the values of the field various points in the medium. To obtain eq. 1.46 in differential form, we will make use of Stoke s theorem, according to which for any vector A having first spatial derivatives, the following relationship holds ... 

The pathways from local markets are much richer. The map shows that complete pathways run from open markets and the farmer to the terminal value. Good relations, via three functional consequences of these choices of outlet. Social contact. Contact with producers, and Advice or service. Contact with producers is a central node where complete pathways for shopping at open markets and direct from the farmer intersect. Thus Contact with producers can be seen to be integral to short organic supply chains (direct and local markets). But, whereas buying from the farmer connects to value only through Contact with producers, shopping in the open market connects to value via Relationship with staff - Advice, and an abstract attribute, Pleasant atmosphere that is linked to both Contact with producers and Social contact. Thus, three main paths can be... 

To calculate the overall ratio between the forward and backward paths we need to integrate P and P over a for a complete period (i.e., from 0 to 1) and take the ratio of their integrals. For each value of a we can use the relation (8) so we have... 

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