Non-relativistic limit of the semi-relativistic Pauli-Fierz model (Mathematical aspects of quantum fields and related topics)

Abstract

The non-relativistic limit of the semi-relativistic Pauli-Fierz Hamiltonian √(c²(-iΔ⊗ 1-A(x))²+m²c⁴) - mc² + V ⊗ 1 + 1 ⊗ H[rad]) is considered. Here c denots the speed of light, m the mass of a charged particle, A a quantized radiation field, V an external potential and H[rad] the free field Hamiltonian. By the limit c → ∞ in the sense of strong semigroup, we derive the Pauli-Fierz Hamiltonian in nonrelativistic quantum electrodynamics: 1/2m (-iΔ⊗ 1-A(x))² + V ⊗ 1 + 1 ⊗ H[rad].