Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit Fermionic Tree Expansions   We express connected Fermionic Green's functions in terms of completely
explicit tree formulas. In contrast with the ordinary formulation in terms of
Feynman graphs these formulas allow a completely transparent proof of
convergence of the perturbative series. Indeed they are compatible with the
mathematical implementation in Grassmann integrals of the Pauli principle. The
first formula we give, which is the most symmetric, is compatible with Gram's
inequality. The second one, the "rooted formula", respects even better the
antisymmetric structure of determinants, and allows the direct comparison of
rows and columns in the fermionic determinant.
  To illustrate the power of these formulas, we provide a ``three lines proof''
that the radius of convergence of the Gross-Neveu field theory with cutoff is
independent of the number of colors. An other potential area for applications
would be the study of correlated Fermions systems and superconductivity.

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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: math
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom