2 00 4 Mass Renormalization in Non - relativistic Quantum Electrodynamics with Spin 1

The effective mass m eff of the the Pauli-Fierz Hamiltonain with ultraviolet cutoff Λ and the bare mass m in nonrelativistic QED with spin 1/2 is investigated. Analytic properties of m eff in coupling constant e are shown and explicit forms of constants a 1 (Λ/m) and a 2 (Λ/m) depending on Λ/m such that m eff /m = 1 + a 1 (Λ/m)e 2 + a 2 (Λ/m)e 4 + O(e 6) are given. It is shown that the spin interaction enhances the effective mass and that there exist strictly positive constants b 1 , b 2 , c 1 and c 2 such that b 1 ≤ lim Λ→∞ a 1 (Λ/m) log(Λ/m) ≤ b 2 , −c 1 ≤ lim Λ→∞ a 2 (Λ/m) (Λ/m) 2 ≤ −c 2. In particular a 2 (Λ/m) does not diverges as ±[log(Λ/m)] 2 but −(Λ/m) 2 .