The two dimensional Hubbard Model at half-filling: I. Convergent Contributions

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We prove analyticity theorems in the coupling constant for the Hubbard model at half-filling. The model in a single renormalization group slice of index i is proved to be analytic in λ for |λ| ≤ c/i for some constant c, and the skeleton part of the model at temperature T (the sum of all graphs without two point insertions) is proved to be analytic in λ for |λ| ≤ c/| T|². These theorems are necessary steps towards proving that the Hubbard model at half-filling is not a Fermi liquid (in the mathematically precise sense of Salmhofer).