Scaling Limits for the System of Semi-Relativistic Particles Coupled to a Scalar Bose Field

TL;DR

This paper investigates the scaling limits of a semi-relativistic particle system coupled to a scalar Bose field, deriving an effective Schrödinger operator in the limit.

Contribution

It introduces a scaled Hamiltonian for semi-relativistic particles interacting with a scalar Bose field and derives the effective Schrödinger operator in the scaling limit.

Findings

Derived the scaled Hamiltonian for the system.

Established the limiting form as an effective Schrödinger operator.

Provided insights into the interaction effects in the scaling limit.

Abstract

In this paper the Hamiltonian for the system of semi-relativistic particles interacting with a scalar bose field is investigated. A scaled total Hamiltonian of the system is defined and its scaling limit is considered. Then the semi-relativistic Schrodinger operator with an effective potential is derived.