Spin-dependent correction to the relativistic-electron mass in QED in the presence of an external electric field |
| |
Authors: | S L Lebedev |
| |
Institution: | 1.Surgut State University,Surgut, Tyumen oblast,Russia |
| |
Abstract: | A new expression is found for the spin-dependent contribution Δm
s
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
⊥|ɛ|/ɛ
c
(γ
⊥2 ≡ 1 + p
⊥2/m
2
c
2 and ɛ
c
≡ m
2
c
3/|e|ℏ) 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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|