Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-07-01
Phys.Rev.D50:7659-7672,1994
Physics
High Energy Physics
High Energy Physics - Theory
29 pages, 3 figures available upon request, Report TPI-MINN-94-24-T Plain LATEX
Scientific paper
10.1103/PhysRevD.50.7659
We consider two-dimensional QED with several fermion flavors on a finite spatial circle. A modified version of the model with {\em flavor-dependent} boundary conditions $\psi_p(L) = e^{2\pi ip/ N} \psi_p(0)$, $p = 1, \ldots , N$ is discussed ($N $ is the number of flavors). In this case a non-contactable contour in the space of the gauge fields is {\em not} determined by large gauge transformations. The Euclidean path integral acquires the contribution from the gauge field configurations with fractional topological charge. The configuration with $\nu = 1/N$ is responsible for the formation of the fermion condensate $\langle\bar{\psi}_p \psi_p\rangle_0$. The condensate dies out as a power of $L^{-1}$ when the length $L$ of the spatial box is sent to infinity. Implications of this result for non-abelian gauge field theories are discussed in brief.
Shifman Michael
Smilga Andrei
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