Abstract
Upcoming experiments on the interaction of electrons with intense laser fields are envisaged to become more and more accurate, which calls for theoretical computations of rates and probabilities with correspondingly higher precision. In strong-field QED this requires the knowledge of radiative corrections to be added to leading-order results. Here, we first derive the mass operator in momentum space of an off-shell electron in the presence of an arbitrary plane wave. By taking the average of the mass operator in momentum space over an on-shell electron state, we obtain a new representation, equivalent to but more compact than the known one computed in [Sov. Phys. JETP \textbf{42}, 400 (1975)]. Moreover, we use the obtained mass operator to determine the electron mass shift in an arbitrary plane wave, which generalizes the already known expression in a constant crossed field. The spin-dependent part of the electron mass shift can be related to the anomalous magnetic moment of the electron in the plane wave. We show that within the locally constant field approximation it is possible to conveniently define a local expression of the electron anomalous magnetic moment, which reduces to the known expression in a constant crossed field. Beyond the locally constant field approximation, however, the interaction between the electron and the plane wave is non-local such that it is not possible to conveniently introduce an electron anomalous magnetic moment.
Highlights
Among the most stringent experimental tests on QED the measurement of the anomalous magnetic moment of either a free [1,2] or a bound [3] electron plays a prominent role
We show that within the locally constant field approximation (LCFA) it is possible to introduce a local expression of the anomalous magnetic moment of the electron, which reduces to the known one in a constant crossed field, already computed in Refs. [82,92]
In the case of an arbitrary plane wave, the electron mass shift features a nonlocal dependence on the plane-wave field, which prevents a convenient description of the spindependent part in terms of an electron anomalous magnetic moment
Summary
Among the most stringent experimental tests on QED the measurement of the anomalous magnetic moment of either a free [1,2] or a bound [3] electron plays a prominent role. [3] electrons bound in highly-charged ions experience electric fields of strengths of the order of the QED scale, the socalled critical electric field of QED Ecr 1⁄4 m2c3=ħjej ≈ 1.3 × 1016 V=cm, with e < 0 and m being the electron charge and mass, respectively [5,6,7,8,9,10] It is desirable, to test the theory in the presence of fields with a different structure and with different properties. We use the spin-dependent part of the mass shift in the case of a linearly polarized plane wave to study the anomalous magnetic moment of the electron. In the case of an arbitrary plane wave, the electron mass shift features a nonlocal dependence on the plane-wave field, which prevents a convenient description of the spindependent part in terms of an electron anomalous magnetic moment
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