On the semigroup generated by the renormalized Nelson Hamiltonian

Abstract

Let us consider the renormalized Nelson model at a fixed total momentum $P$: $H_{\mathrm{ren}}(P)$; The Hamiltonian $H_{\mathrm{ren}}(P)$ is defined through an infinite energy renormalization. We prove that $e^{-\beta H_{\mathrm{ren}}(P)}$ is positivity improving for all $P\in {\mathbb{R}}^3$ and $\beta >0$ in the Fock representation.

V2: Revised version

References in corpus (1)

• On the domain of the Nelson Hamiltonian