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Abstract

The value of the anomalous magnetic moment of the electron is the most accurately
verified prediction of Quantum Electrodynamics (QED). Upcoming QED
experiments on the interaction of electrons with intense laser fields open up the
way of checking whether this high degree of agreement for the value of the electron
anomalous magnetic moment persists in intense background fields. The
possibility of experimentally verifying the expression for the anomalous magnetic
moment of the electron in intense laser fields calls for computing radiative corrections
beyond the leading-order result, that already includes the background field
exactly. While in vacuum QED the anomalous magnetic moment is extracted
from the vertex diagram for which the external photon provides the magnetic
field interacting with the electron, in the strong field case the mass operator is
used, where the magnetic field of the plane wave is exploited instead. Hence,
in the thesis, the renormalized momentum space mass operator for an off-shell
electron in the presence of an arbitrary plane-wave background is computed in
light-cone coordinates, which have the advantage of making transparent the conserved
quantities. Sandwiching between on-shell electron states, a new representation,
more compact than the one known from the literature [VS75], is obtained.
Solving the Schwinger-Dyson equation for the electron, in which the determined
mass operator is inserted, the electron mass shift in an arbitrary plane wave is obtained.
The expression for the electron mass shift generalizes the already known
expressions from the literature [VS71; Rit70] for the constant crossed field case.
The spin-dependent part of the electron mass shift is related to the anomalous
magnetic moment of the electron in the plane wave. In the locally constant field
approximation, the anomalous magnetic moment of the electron is extracted and
reduces to Schwinger’s famous result when the background is removed. However,
due to the non-local dependence of the electron mass shift on the field, it is not
generally possible to define a local expression of the electron anomalous magnetic
moment in an arbitrary plane