The Nelson Model on Static Spacetimes

TL;DR

This paper extends the Nelson model, which describes particle-field interactions, to static spacetimes using a novel interior boundary condition approach for defining the Hamiltonian.

Contribution

It applies recent techniques involving interior boundary conditions to define the Nelson Hamiltonian on static spacetimes, advancing the mathematical understanding of quantum field interactions in curved backgrounds.

Findings

Successfully extended the Nelson model to static spacetimes.

Established a Fock space description using interior boundary conditions.

Provided a rigorous mathematical framework for the model in curved spacetime.

Abstract

The Nelson model describes the interaction of nonrelativistic quantum particles with a relativistic quantum field of scalar bosons. Nelson rigorously demonstrated in 1964 the existence of a well-defined self-adjoint Nelson Hamiltonian by renormalisation. Recently, a Fock space description of the renormalised Nelson Hamiltonian and its domain were found based on a novel approach to defining Hamiltonians in quantum field theories. This novel approach involves an interior boundary condition (IBC) on the state vectors, which relates the value of the wave function on the boundary of the configuration space to the value at a point in the interior. In the present work, we apply the recently developed techniques to the Nelson model on static spacetimes.