Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-10-30
Annals Phys. 255 (1997) 333-361
Physics
High Energy Physics
High Energy Physics - Theory
One reference added plus one corrected, final version as to be published in Annals of Physics
Scientific paper
10.1006/aphy.1996.5664
The $N_f$-flavour Schwinger Model on a finite space $0\leq x^1\leq L$ and subject to bag-type boundary-conditions at $x^1=0$ und $x^1=L$ is solved at finite temperature $T=1/\beta$. The boundary conditions depend on a real parameter $\theta$ and break the axial flavour symmetry. We argue that this approach is more appropriate to study the broken phases than introducing small quark masses, since all calculations can be performed analytically. In the imaginary time formalism we determine the thermal correlators for the fermion-fields and the determinant of the Dirac-operator in arbitrary background gauge-fields. We show that the boundary conditions induce a CP-odd $\theta$-term in the effective action. The chiral condensate, and in particular its T- and L- dependence, is calculated for $N_f$ fermions. It is seen to depend on the order in which the two lengths $\beta=1/T$ and $L$ are sent to infinity.
Dürr Stephan
Wipf Andreas
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