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    The Stochastic Quantization Method in Phase Space and a New Gauge Fixing Procedure

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    We study the stochastic quantization of the system with first class constraints in phase space. Though the Langevin equations of the canonical variables are defined without ordinary gauge fixing procedure, gauge fixing conditions are automatically selected and introduced by imposing stochastic consistency conditions upon the first class constraints. Then the equilibrium solution of the Fokker-Planck equation is identical with corresponding path integral distribution.Comment: 18 pages (Plain TeX), CHIBA-EP-7

    Asymptotic behaviour of certain families of harmonic bundles on Riemann surfaces

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    Let (E,E,θ)(E,\overline{\partial}_E,\theta) be a stable Higgs bundle of degree 00 on a compact connected Riemann surface. Once we fix the flat metric hdet(E)h_{\det(E)} on the determinant of EE, we have the harmonic metrics hth_t (t>0)(t>0) for the stable Higgs bundles (E,E,tθ)(E,\overline{\partial}_E,t\theta) such that det(ht)=hdet(E)\det(h_t)=h_{\det(E)}. We study the behaviour of hth_t when tt goes to \infty. First, we show that the Hitchin equation is asymptotically decoupled under the assumption that the Higgs field is generically regular semisimple. We apply it to the study of the so called Hitchin WKB-problem. Second, we study the convergence of the sequence (E,E,θ,ht)(E,\overline{\partial}_E,\theta,h_t) in the case where the rank of EE is two. We introduce a rule to determine the parabolic weights of a "limiting configuration", and we show the convergence of the sequence to the limiting configuration in an appropriate sense. The results can be appropriately generalized in the context of Higgs bundles with a Hermitian-Einstein metric on curves
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