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Resumen:
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The imaginary time generating functional Z for the assless Schwinger model at nonzero chemical potential mu and temperature T is studied in a torus with spatial length L. The lack of Hermiticity of the Dirac operator gives rise to a nontrivial ?- and T-dependent phase J in the effective action. When the Dirac operator has no zero modes (trivial sector), we evaluate J, which is a topological contribution, and we find exactly Z, the thermodynamical partition function, the boson propagator and the thermally averaged Polyakov loop. The ?-dependent contribution of the free partition function cancels exactly the nonperturbative one from J, for L??, yielding a zero charge density for the system, which bosonizes at nonzero ?. The boson mass is e/??, independent of T and ?, which is also the inverse correlation length between two opposite charges. Both the boson propagator and the Polyakov loop acquire a new T- and ? -dependent term at L??,. The imaginary time generating functional for the massless Thirring model at nonzero T and ? is obtained exactly in terms of the above solution of the Schwinger model in the trivial sector. For this model, the ? dependences of the thermodynamical partition function, the total fermion number density and the fermion two- point correlation function are obtained. The phase J displayed here leads to our new results and allows us to complement nontrivially previous studies on those models.
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