Caustics in the Grassmann Integral

Details Caustics in the Grassmann Integral Caustics in the Grassmann Integral

2003-01-06

arxiv.org/abs/hep-th/0301019v2

Prog.Theor.Phys. 110 (2003) 589-603

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, 6 figures and 3 tables

Scientific paper

10.1143/PTP.110.589

It is shown that a simple model of 2N-Grassmann variables with a four-body coupling involves caustics when the integral has been converted to a bosonic form with the aid of the auxiliary field. Approximation is then performed to assure validity of the auxiliary field method(AFM). It turns out that even in N=2, the smallest case in which a four-body interaction exists, AFM does work more excellently if higher order effects, given by a series in terms of $1/N^{1/3}$ around a caustic and of 1/N around a saddle point, would be taken into account.

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