Ultraviolet Renormalisation of a quantum field toy model I

Abstract

We consider a class of Hamiltonians describing a fermion field coupled to a boson field. The interaction kernels are assumed bounded in the fermionic momentum variable and decaying like $|q{|}^{-p}$ for large boson momenta $q$. A realistic physical case would be $p=\frac{1}{2}$. We impose a spatial cutoff and UV-renormalise the resulting Hamiltonian by subtracting its ground state energy. Our renormalisation procedure works for the physically realistic value $p=\frac{1}{2}$ in spatial dimensions $1$ and $2$ and for $p>\frac{3}{4}$ in spatial dimension $d=3$.

References in corpus (2)

• Asymptotic Completeness in Quantum Field Theory: Translation Invariant Nelson Type Models Restricted to the Vacuum and One-Particle Sectors
• On the domain of the Nelson Hamiltonian