Four-point Green functions in the Schwinger Model

Details Four-point Green functions in the Schwinger Model Four-point Green functions in the Schwinger Model

1998-09-17

arxiv.org/abs/hep-th/9809129v1

Phys.Rev. D59 (1999) 065010

Physics

High Energy Physics

High Energy Physics - Theory

In Revtex, 12 pages + 2 PostScript figures

Scientific paper

10.1103/PhysRevD.59.065010

The evaluation of the 4-point Green functions in the 1+1 Schwinger model is presented both in momentum and coordinate space representations. The crucial role in our calculations play two Ward identities: i) the standard one, and ii) the chiral one. We demonstrate how the infinite set of Dyson-Schwinger equations is simplified, and is so reduced, that a given n-point Green function is expressed only through itself and lower ones. For the 4-point Green function, with two bosonic and two fermionic external `legs', a compact solution is given both in momentum and coordinate space representations. For the 4-fermion Green function a selfconsistent equation is written down in the momentum representation and a concrete solution is given in the coordinate space. This exact solution is further analyzed and we show that it contains a pole corresponding to the Schwinger boson. All detailed considerations given for various 4-point Green functions are easily generizable to higher functions.

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