Institute of Mathematics for Industry

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A new asymptotic perturbation theory and applications to massless quantum field theories


Hold Date 2013-01-17 16:00~2013-01-17 17:30

Place Seminar Room 7, Faculty of Mathematics building, Ito Campus

Object person  

Speaker ARAI, Asao (Hokkaido University)

Abstract:
The standard analytic or asymptotic perturbation theory considers only perturbations of isolated eigenvalues. In this lecture, we present a new asymptotic perturbation theory which may be valid also for the case where the unperturbed operator has a non-isolated eigenvalue (important examples in which the unperturbed operator has non-isolated eigenvalues appear, e.g., in massless quantum field theories). As an application, we consider a quantum  field model, called the generalized spin-boson model (including the massless case), and, for its ground state energy,  we derive an asymptotic expansion in the coupling constant up to an arbitrary finite order.