Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-12-13
Phys.Rev. D51 (1995) 7060-7082
Physics
High Energy Physics
High Energy Physics - Theory
44 pages; for hardcopies of figures, contact thies@theorie3.physik.uni-erlangen.de
Scientific paper
10.1103/PhysRevD.51.7060
A study of two-dimensional QCD on a spatial circle with Majorana fermions in the adjoint representation of the gauge groups SU(2) and SU(3) has been performed. The main emphasis is put on the symmetry properties related to the homotopically non-trivial gauge transformations and the discrete axial symmetry of this model. Within a gauge fixed canonical framework, the delicate interplay of topology on the one hand and Jacobians and boundary conditions arising in the course of resolving Gauss's law on the other hand is exhibited. As a result, a consistent description of the residual $Z_N$ gauge symmetry (for SU(N)) and the ``axial anomaly" emerges. For illustrative purposes, the vacuum of the model is determined analytically in the limit of a small circle. There, the Born-Oppenheimer approximation is justified and reduces the vacuum problem to simple quantum mechanics. The issue of fermion condensates is addressed and residual discrepancies with other approaches are pointed out.
Lenz Florian
Shifman Michael
Thies Michael
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