Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-05-10
Phys.Rev. D54 (1996) 7794-7814
Physics
High Energy Physics
High Energy Physics - Theory
24 pages, uses REVTEX macros. Replaced with final version to appear in Phys. Rev. D
Scientific paper
10.1103/PhysRevD.54.7794
In this paper, colorless bilocal fields are employed to study the large $N$ limit of both fermionic and bosonic vector models. The Jacobian associated with the change of variables from the original fields to the bilocals is computed exactly, thereby providing an exact effective action. This effective action is shown to reproduce the familiar perturbative expansion for the two and four point functions. In particular, in the case of fermionic vector models, the effective action correctly accounts for the Fermi statistics. The theory is also studied non-perturbatively. The stationary points of the effective action are shown to provide the usual large $N$ gap equations. The homogeneous equation associated with the quadratic (in the bilocals) action is simply the two particle Bethe Salpeter equation. Finally, the leading correction in $1\over N$ is shown to be in agreement with the exact $S$ matrix of the model.
Mello Koch Robert de
Rodrigues Joao P.
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