Suggestion for a fingerprint

Basic idea: Instead of a name or data-set which uniquely defines a given Feynman graph, a fingerprint is a simple sequence of numbers and letters, capturing only some information of the graph, but hopefully enough to find satisfying results in the database.

For example, a fingerprint of a graph G may be the sequence:


L: loop-number of the graph,
E: number of legs,
S: sequence of vertex-degrees, where each number is written N times if G has N vertices with that degree; sequence starts with highest degree,
(convention: degree means, number of internal edges attached to the vertex),
M: number of massive propagators,
O: optional information

Let G be the scalar double-box graph as computed by Smirnov in 1999.
The graph has two loops, four legs, two vertices with degree 3, four vertices with degree 2, no masses.
From this information we build up the above fingerprint as:
We have omitted the last entry of optional information for now.

The database of bibliographical references (and, maybe later, for results) could be organized such that it can be searched for this fingerprint. In the above example, the input of the search would be the sequence 2.4.332222.0. The output would be a list of all references with results of graphs with this fingerprint. The list would contain the article by Smirnov.

The fingerprint construction must be set up such that each graph has a unique fingerprint (as in the above suggestion), but it is hard (or impossible) to set up a construction, such that for each fingerprint there is a unique graph. Instead of trying to get there, it may be better to keep the conventions rather simple, such that everybody can construct the fingerprint of the desired graph by hand, within a few seconds. The disadvantage of such a simple construction is that several graphs may have the same fingerprint. In the above example, not only the desired planar double-box of Smirnov would be found, but also the non-planar double-box, as computed by Tausk in 1999, because, by the above conventions, both graphs have the same fingerprint.

One may partly improve on this by adding the optional information O. This might be simply a letter, indicating some additional information of the graph, for example N for non-planar and P for planar graphs. Then the planar and non-planar double-boxes would have the fingerprints 2.4.332222.0.P and 2.4.332222.0.N respectively, and the search for these sequences would give either Smirnov's or Tausk's paper, but not both. (The user should still be free to omit the additional information, search only for 2.4.332222.0, and obtain both results.)

It may be an interesting challenge to construct a fingerprint convention better than the above. The requirements could be:

  • easy to construct by the user,
  • not too many non-isomorphic graphs per fingerprint,
  • data of physical relevance (such as number of loops and legs) is preferred to more formal data (such as vertex degrees),
  • there is an ordering on the set of all fingerprints

Another advantage: If after a while a fingerprint convention would be widely accepted in the community, one could also search the arxiv or spires for these sequences.

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