Spin-dependent correction to the relativistic-electron mass in QED in the presence of an external electric field

摘要

A new expression is found for the spin-dependent contribution Δms to the self-energy of an electron moving with a transverse momentum p⊥ in an electric field. The structure of an asymptotic expansion of Δm_s(r, χ) as a function of two dynamical invariants r = γ⊥~(-2) and χ = γ⊥{pipe}e{open}{pipe}/e{open}_c (γ⊥~2≡ 1 + p⊥~2/m~2c~2 and e{open}_c ≡ m~2c~3/{pipe}e{pipe}h{stroke}) is clarified with the aid of this expression. The expansion of Δm_s(r, χ) can be represented in the form of a Taylor series in r, the coefficients in this series, F_0(χ), F_1(χ), etc., being integrals of the Mellin type. The major coefficient F_0(χ) is universal and, in the case of an appropriate interpretation of χ, describes well-known spin-dependent corrections to the mass in three different cases of a constant external field (for r → 0). The asymptotic properties of the function F_1(χ) are studied in detail, but only order-of-magnitude estimates are obtained for F_2(χ) and F_3(χ). A comparison of these contributions revealed that, in the semiclassical region χ ? 1, r is indeed the parameter of the aforementioned expansion, while, for χ ? 1, the true parameter is rχ~2 ≡ β~2. In particular, the anomalous magnetic moment develops, owing to F_1(χ), a term that grows logarithmically for χ ? 1, but which does not violate the hierarchy of terms in the Taylor series being considered, provided that β remains smaller than unity.