Exact Solution of the Schwinger Model with Compact U(1)

Details Exact Solution of the Schwinger Model with Compact U(1) Exact Solution of the Schwinger Model with Compact U(1)

2001-03-08

arxiv.org/abs/hep-th/0103057v1

Mod.Phys.Lett. A16 (2001) 121-134

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, 2 figures. Accepted for publication in Mod. Phys. Letts. A

Scientific paper

10.1142/S0217732301003152

The exact solution of the Schwinger model with compact gauge group U(1) is presented. The compactification is imposed by demanding that the only surviving true electromagnetic degree of freedom has angular character. Not surprinsingly, this topological condition defines a version of the Schwinger model which is different from the standard one, where $c$ takes values on the line. The main consequences are: the spectra of the zero modes is not degenerated and does not correspond to the equally spaced harmonic oscillator, both the electric charge and a modified gauge invariant chiral charge are conserved (nevertheless, the axial-current anomaly is still present) and, finally, there is no need to introduce a $\theta$-vacuum. A comparison with the results of the standard Schwinger model is pointed out along the text.

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