Mass Renormalization in the Nelson Model

Abstract EN

The asymptotic behavior of the effective mass meff(Λ) of the so-called Nelson model in quantum field theory is considered, where Λ is an ultraviolet cutoff parameter of the model.

Let m be the bare mass of the model.

It is shown that for sufficiently small coupling constant α of the model, meff(Λ)/m can be expanded as meff(Λ)/m=1+∑n=1∞an(Λ)α2n.

A physical folklore is that an(Λ)=O(logΛ(n-1)) as Λ→∞.

It is rigorously shown that 0