content_image/440339.jpg
The integration over momenta can be carried out explic- itly and we finally obtain a path integral in the configu- ration space only (tildes are removed from the position variables), 

<img src='content_image/440339.jpg'>

This formula served us as a guide when introducing the 

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Let us make one final comment. In our functional measure (B5) no integration over the momenta p$_{(0}$$_{,σ}$$_{)}$ and p$_{(}$$_{K,σ}$$_{)}$ was prescribed. These momenta are how- ever needed when the boundary of the discretized surface Σ ∈ U$_{γ}$$_{cl}$ is specified. They define the auxiliary curves λ$_{0}$ ( s ) and λ$_{1}$ ( s ) introduced in section III. The curves were chosen completely arbitrarily, but as seen from (B4), the result is not affected by them at all. Hence, since every- thing substantial is independent of p$_{(0}$$_{,σ}$$_{)}$ and p$_{(}$$_{K,σ}$$_{)}$ , it is justifiable to discard these quantities from the functional measure [ D Σ] . If we would not do that for some reason, they will integrate into an artificial infinite factor, which will be removed anyway after we apply the normalization conditions (2). 

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