A Technique for generating Feynman Diagrams

We present a simple technique that allows to generate Feynman diagrams for vector models with interactions of order $2n$ and similar models (Gross-Neveu, Thirring model), using a bootstrap equation that uses only the free field value of the energy as an input. The method allows to find the diagrams to, in principle, arbitrarily high order and applies to both energy and correlation functions. It automatically generates the correct symmetry factor (as a function of the number of components of the field) and the correct sign for any diagram in the case of fermion loops. We briefly discuss the possibility of treating QED as a Thirring model with non-local interaction.Comment: 19 pages, LateX, To be published in Z. f. Phys.

Large N limit of O(N) vector models

Using a simple identity between various partial derivatives of the energy of the vector model in 0+0 dimensions, we derive explicit results for the coefficients of the large N expansion of the model. These coefficients are functions in a variable $\rho^2$, which is the expectation value of the two point function in the limit $N=\infty$. These functions are analytic and have only one (multiple) pole in $\rho^2$. We show to all orders that these expressions obey a given general formula. Using this formula it is possible to derive the double scaling limit in an alternative way. All the results obtained for the double scaling limit agree with earlier calculations. (to be published in Physics Letters B)Comment: 12 page