Feynman Integrals: symmetries and seagulls

Feynman diagrams will be looked at from a new point of view Symmetries of Feynman Integrals is an analytical method for calculating Feynman diagrams It is based on exposing an underlying group structure of a given diagram which defines a set of partial differential equations in the parameter space of the diagram Group orbits in the diagram s parameter space are used to reduce the Feynman integral into a line integral The vacuum seagull a three loop diagram and the propagator seagull a propagator type diagram with two loops will be used to demonstrate the method and to obtain new results