Hokkaido Mathematical Journal

OHKUBO Atsushi,

Scaling limit for the Derezi\'nski-G\'erard model.

Hokkaido Mathematical Journal, 39 (2010) pp.261-290

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Abstract

We consider a scaling limit for the Derezi\'nski-G\'erard model. We derive an effective potential by taking a scaling limit for the total Hamiltonian of the Derezi\'nski-G\'erard model. Our method to derive an effective potential is independent of whether or not the quantum field has a nonnegative mass. As an application of our theory developed in the present paper, we derive an effective potential of the Nelson model.

MSC(Primary)81T10
MSC(Secondary)
Uncontrolled KeywordsFock space, scaling limit, effective potential, the Derezi\'nski-G\'erard model, the Nelson model, Weyl relations