The structure of Green functions in quantum field theory with a non-Gaussian measure

In quantum field theory with a non-Gaussian measure, the Green functions are described by Feynman diagrams that are built, not only from a single two-legged free propagator g(x,y), but from n-legged free propagators, where n is any natural number. This increases considerably the combinatorial difficulty of the theory.

Moreover, in the application of non-Gaussian QFT to many-body physics, all n-legged free propagators with n different from 2 are solutions of the free Schroedinger equation. Therefore, we are not allowed to use the inverse of g(x,y) to amputate Green functions because this would kill non-Gaussian contributions to the Green function. As a consequence, computational methods based on the Legendre transformation are not available.

For these reasons, the structure of non-Gaussian Green functions were poorly investigated despite their importance for the calculation of strongly-correlated systems. In this talk, the Hopf algebraic methods developed by Fauser, Frabetti, Oeckl and Mestre will be used to solve this problem.