The anomalous magnetic moment of the electron

The value of the electron's magnetic moment is a fundamental quantity in physics. Its deviation from the value expected from Dirac theory has given enormous impetus to the field of quantum theory and especially to quantum electrodynamics (QED) as the relativistic quantum field theory of electrodynamics. In fact, the measured values both for free and for bound electrons are explained by corresponding QED calculations on the part per trillion and part per billion level of accuracy, respectively. This agreement is amongst the best known in physics today. In turn, it allows highly precise determinations of related fundamental constants like the fine structure constant α or the electron mass. The present article discusses the application of the continuous Stern–Gerlach effect to the precise measurement of magnetic moments, especially of the electron bound in highly charged ions and possible tests of calculations in the framework of QED of bound states. Also, a test of QED in a more general approach by the comparison of values for the fine structure constant derived from different measurements, will be discussed.     

Contributions of weak and strong interactions to the anomalous magnetic moment of the electron

Based on Weinberg - Salam weak interaction theory, we have determined the addition to the anomalous magnetic moment of the electron arising from interaction between the electron and quantum fluctuations of the vector field (the carrier of the weak interaction). We also estimate the contribution of the strong interaction to the anomalous magnetic moment of the electron due to polarization of the quark — gluon vacuum. The overall contribution of the weak and strong interactions to the anomalous magnetic moment proves to be equal to 1·10^–12, and the contribution of the weak interaction is 2.2 times greater than the contribution of the strong interaction.Kamskii Polytechnical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 13–19, November, 1993.     

The anomalous magnetic moment of the electron in hydrogenlike ions

The precise determination of the anomalous magnetic moment of the electron bound in hydrogen-like ions allows for a stringent test of quantum electrodynamics (QED)in the presence of strong electric fields. g-factor measurements on the electron bound in hydrogen-like ions ¹²C⁵⁺ and ¹⁶O⁷⁺, using single ions confined in a Penning trap, have yielded values in agreement with theory on the ppb level. If the QED calculations are considered correct, the results can in turn be used for a determination of fundamental constants like the electron mass m_e, the fine structure constant α or nuclear parameters. We report about presentdevelopments towards g-factor measurements also in medium-heavy and heavy highly-charged ions.     

Quasi-two-dimensional electron gas in a non-quantizing magnetic field and strong non-quantizing electric field

A calculation is performed to determine the transverse electric field E_y formed in quasi-two-dimensional superlattices in a strong drift field E_x and a weak magnetic field that is perpendicular to the plane of the superlattice (H‖OZ). When the electronic energy spectrum is nonadditive, the field E_y includes both the Hall factor and a spontaneous transverse electric field that exists whetherH is present or not. The situation when the specimen is in a closed circuit with a resistor on the OY axis is examined. As the function E_x, the field E_y is multivalued (multistable) and variable. The stability of the branches of the function E_y(E_x) is determined using a specially introduced (kinetic) “potential” whose minimum corresponds to the steady state of a nonequilibrium electron gas. Volgograd State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 46–51, July, 1996.     

Motion of dirac particles possessing an anomalous magnetic moment in a centrally symmetric electric field

States of a relativistic electron having an anomalous magnetic moment and moving in a centrally symmetric field are classified by a method most similar to a nonrelativistic classification. A spin quantum number is clearly defined. The motion of a neutron in a central field is also investigated. Some new, exact solutions of the Dirac-Pauli equation are found. A classical interpretation of the results is conducted.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 38–45, November, 1971.     

Induced radiation by electron with anomalous magnetic moment in the field of a plane electromagnetic wave

The dependence is investigated on the induced electron radiation with an anomalous magnetic moment moving in the field of a plane circularly-polarized electromagnetic wave of the polarization, frequency and intensity of another wave which excites the system. It is shown that if one takes into account the anomality of a magnetic moment of the electron this results in frequency shift, change in power and spin effect.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 28–33, April, 1972.The authors are grateful to Professor V. G. Bagrov for the interest he has taken in this work.     

On the interpretation of the electron anomalous magnetic moment

Guided by a Compton-sized model, we demonstrate that: (a) the magnetic self-energy of the electron, as estimated initially by Rasetti and Fermi, can be directly related to both the sign and the magnitude of the electron anomalous magnetic moment; and (b) the classical expression for the magnetic self-energy of the electron exhibits the same characteristic logarithmic divergence that occurs in QED. This electron model quantitatively reproduces the spin, magnetic moment, and gyromagnetic ratio of the electron, correct to first order in = e² /c. It also relates the quantum-mechanical spin projection angle to the vanishing of the electric quadrupole moment, and it is capable of reproducing point-like scattering behavior.     

Dirac particle with an anomalous magnetic moment in a circularly polarized wave and in constant longitudinal magnetic and electric fields

The wave function of an uncharged Dirac particle with an anomalous magnetic moment is calculated for the case where a circularly polarized wave propagating along constant magnetic and electric fields is present. Zh. éksp. Teor. Fiz. 111, 1190–1193 (April 1997)     

Effective coupling constant expansion of the muon anomalous magnetic moment

The relationship between the renormalization group and the muon anomalous magnetic moment calculation in QED is reconsidered. A very simple analysis shows that the contribution to the muon anomaly from muon vertex graphs with electron loop insertions in the photon propagators is function of only one dimensionless effective coupling constant $\text{α}{}_{\mathrm{\mu }}\text{?}\text{1}\text{136.0785}$. The perturbative expansion coefficients up to the α³_μ term are given, and comparison is made with the previous calculations.     

The short distance behaviour of the anomalous magnetic moment of the electron

The effective anomalous magnetic moment of the electron vanishes at short distances because the electrodynamic form factor F₂(q²) vanishes for |q²| → ∞. The effective potential due to the interaction between the anomalous magnetic moment and the Coulomb field of a nucleus only diverges logarithmically at short distances, and not, as might naively be expected, quadratically. There are no other bound states of an electron in a Coulomb field than the well-known atomic states. In particular, there is no room for high mass resonances emulating the ψ as suggested by Barut and Kraus.     

The spin and the anomalous magnetic moment of the electron in stochastic electrodynamics

It is proposed that the zitterbewegung induced on a harmonically bound electron by the zero-point radiation field accounts for the spin of the electron. Assuming that the measurement of a spin projection may be taken into account phenomenologically by considering the action of only the subensemble of the zero-point field with the corresponding circular polarization, the theory gives a satisfactory account of both the spin projection and the anomalous magnetic moment.     

Interacting electron gas in a strong magnetic field

The density response function of an electron gas in a strong magnetic field shows logarithmic singularities due to scattering across the Fermi surface. We analyze the parquet equations for the vertex function in leading logarithmic order for a general interaction potential. The parquet equations are solved for a special interaction potential (Schulz and Keiter model). The divergence of the density response function at extremely high fields is discussed in connection with a possible transition to a Wigner lattice.     

The electron effective mass under strong electric field

The electron effective mass dependence on the high static electric field has been found. The dependence is determined by the field effect on the scattering processes of electrons. The mechanism of “impurity” self-induced transparence of conductors is considered for the case of intense high-frequency electric field.     

A sixth order contribution to the electron anomalous magnetic moment

We evaluate analytically the contribution to the anomalous magnetic moment of the electron due to a set of sixth order graphs with two crossed photon lines. The dimensional regularization is used to parametrize the spurious infrared divergences.     

A new value of the anomalous magnetic moment of the electron

The contribution to the sixth order anomaly a_e⁽⁶⁾ from light-by-light scattering subgraphs is recomputed. The result is: a_e^γ?γ = (α³/π³)(0.366 ± 0.010). This result agrees with a previous calculation done at SLAC. The accuracy is improved by a factor of 4. With the currently accepted values for many of the other diagrams, the sixth order anomaly is a_e⁽⁶⁾ = (1.16 ± 0.07) (σ/π)³.     

Vacuum magnetic moment of an electron moving in a uniform magnetic field

The methods of quantum electrodynamics are used to study the dependence of the vacuum magnetic moment of the electron on its energy and on the magnetic field intensity. This dependence is most important in the case of strong magnetic fields. For an ultrarelativistic electron, the vacuum magnetic moment turns out to depend on the electron energy, even in a weak magnetic field.Translated from Izvestiya VUZ. Fizika, Vol. 11, No. 11, pp. 17–22, November, 1968.