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Polyakov loops and fermionic zero-modes in QCD\(_2\) on the torus. (English) Zbl 0945.81024

Summary: A direct derivation of the free energy and expectation values of Polyakov loops in QCD\(_2\) via path integral methods is given. The chosen gauge fixing has no Gribov copies and has a natural extension to four dimensions. The Faddeev-Popov determinant and the integration over the space component of the gauge field cancel exactly. It only remains an integration over the zero components of the gauge field in the Cartan subalgebra. This way the Polyakov-loop operators become vertex operators in a simple quantum mechanical model. The number of fermionic zero-modes is related to the winding numbers of \(A_0\) in this gauge.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T10 Model quantum field theories
81V05 Strong interaction, including quantum chromodynamics
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