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

Journal Article · Tue Mar 15 04:00:00 EDT 2011 · Physics of Atomic Nuclei

DOI:https://doi.org/10.1134/S1063778811030136· OSTI ID:22029939

A new expression is found for the spin-dependent contribution {Delta}m{sub s} to the self-energy of an electron moving with a transverse momentum p Up-Tack in an electric field. The structure of an asymptotic expansion of {Delta}m{sub s}(r, {chi}) as a function of two dynamical invariants r = {gamma}{sub Up-Tack }{sup -2} and {chi} = {gamma}{sub Up-Tack} vertical bar {epsilon} vertical bar /{epsilon}{sub c} ({gamma}{sub Up-Tack }{sup 2} {identical_to} 1 + p{sub Up-Tack }{sup 2}/m{sup 2}c{sup 2} and {epsilon}{sub c} {identical_to} m{sup 2}c{sup 3}/ vertical bar e vertical bar Planck-Constant-Over-Two-Pi ) is clarified with the aid of this expression. The expansion of {Delta}m{sub s}(r, {chi}) can be represented in the form of a Taylor series in r, the coefficients in this series, F{sub 0}({chi}), F{sub 1}({chi}), etc., being integrals of the Mellin type. The major coefficient F{sub 0}({chi}) is universal and, in the case of an appropriate interpretation of {chi}, describes well-known spin-dependent corrections to the mass in three different cases of a constant external field (for r {yields} 0). The asymptotic properties of the function F{sub 1}({chi}) are studied in detail, but only order-of-magnitude estimates are obtained for F{sub 2}({chi}) and F{sub 3}({chi}). A comparison of these contributions revealed that, in the semiclassical region {chi} Much-Less-Than 1, r is indeed the parameter of the aforementioned expansion, while, for {chi} Much-Greater-Than 1, the true parameter is r{chi}{sup 2} {identical_to} {beta}{sup 2}. In particular, the anomalous magnetic moment develops, owing to F{sub 1}({chi}), a term that grows logarithmically for {chi} Much-Greater-Than 1, but which does not violate the hierarchy of terms in the Taylor series being considered, provided that {beta} remains smaller than unity.

• OSTI ID: 22029939
• Journal Information: Physics of Atomic Nuclei, Journal Name: Physics of Atomic Nuclei Journal Issue: 3 Vol. 74; ISSN 1063-7788; ISSN PANUEO
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ASYMPTOTIC SOLUTIONS
COMPARATIVE EVALUATIONS
CORRECTIONS
ELECTRIC FIELDS
ELECTRONS
MAGNETIC MOMENTS
QUANTUM ELECTRODYNAMICS
RELATIVISTIC RANGE
REST MASS
SELF-ENERGY
SEMICLASSICAL APPROXIMATION
SPIN
TRANSVERSE MOMENTUM