Scalar Feynman Diagrams and Symanzik Polynomials
Scalar Feynman Diagrams and Symanzik Polynomials
This Demonstration allows the construction of an arbitrary Feynman graph and displays its position space, momentum space, or parametrized amplitude. For simplicity, it assumes a Euclidean scalar field theory with dimensional regularization and only allows single powers of the propagators. External momenta can be toggled on and off and are always considered incoming. Edge contraction and deletion are available by clicking an edge in the left-hand panel. In particular, the sequence of two-loop propagator graphs in the bookmarks is obtained via successive edge contractions of the highest numbered edge.
The principal purpose of this Demonstration is the calculation of the Symanzik polynomials for arbitrary scalar graphs. These are used in both the Feynman and Schwinger parametrizations of a graph's amplitude.