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Enhanced Binding for the semi-relativistic Nelson Model

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Enhanced Binding for the semi-relativistic Nelson Model

Itaru Sasaki Shinshu University

September 2011

We consider a system of semi-relativistic N particles interacting with a scalar bose field under influences of an external potentialV. TheN-particles do not directly interact each other but interact through the bose field. The effective potential of the particles is derived by a scaling limit of the total Hamiltonian. We assume that V is sufficiently small such that the semi- relativistic Schr¨odinger operator √

−∆ +m2 −m +V(x) has no negative energy ground state. Hence the total system has no ground state if there is no particle-boson interaction. We establish the ground state of the total system by using an information of the effective potential. This is joint work with Fumio Hiroshima(Kyushu university).

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