Spectral analysis of quantum field theory by means of functional integrations

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According to purpose(I),(II) and(III) proposed in KENKYU-KEIKAKU-CHOSHO, we review results obtained by Grant-in-Aid for Challenging Exploratory Research.(I) The functional integral representation of the heat semi-group generated by the relativistic PF model is constructed in terms of three stochastic processes, Euclidean field, Brownian motion and subordinator. By using this we show the essential self-adjointness of PF model, decay of bound states and the uniqueness of ground state.(II) Enhanced binding of the many-body relativistic Nelson model is shown with Itaru Ssasaki(Shinshu university). A functional integral representation is a key ingredient. The result was sent to an international journal for publication.(III) The Nelson model defined on a pseudo Riemannian manifold is studied with C. Gerard(Paris XI), Akito Suzuki(Shinshu university) and Annalisa Panati(Toulon-Var). We published papers in international journals.