Scaling Limit of Quantum Electrodynamics with Spatial Cutoffs

TL;DR

This paper investigates the asymptotic behavior of the Hamiltonian in quantum electrodynamics with spatial cutoffs, demonstrating its convergence to a self-adjoint operator and deriving effective potentials.

Contribution

It introduces a scaled Hamiltonian for QED with spatial cutoffs and proves its strong resolvent convergence, providing new insights into the model's limiting behavior.

Findings

Scaled Hamiltonian converges to a self-adjoint operator

Effective potentials are derived in the limit

Provides rigorous mathematical foundation for QED with cutoffs

Abstract

In this paper the Hamiltonian of quantum electrodynamics with spatial cutoffs is investigated. We define a scaled total Hamiltonian and consider its asymptotic behavior. In the main theorem, it is shown that the scaled total Hamiltonian converges to a self-adjoint operator in the strong resolvent sense, and effective potentials are derived.