Explicit Fermionic Tree Expansions

Details Explicit Fermionic Tree Expansions Explicit Fermionic Tree Expansions

1997-12-04

arxiv.org/abs/cond-mat/9712055v2

Physics

Condensed Matter

Superconductivity

11 pages, 1 figure

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Explicit Fermionic Tree Expansions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Explicit Fermionic Tree Expansions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Explicit Fermionic Tree Expansions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-220872