Magnetism quantum electrodynamic theory

These three examples reflect various aspects of quantum electrodynamics theory. The electron anomalous magnetic moment follows from free-electron QED, the transition frequencies in hydrogen follow from bound-state QED, and, at least in principle, the relevant condensed matter theory follows from the equations of many-body QED. 

The anomalous contribution to the magnetic moment of an electron has been explained by the quantum electrodynamic theory. The additional contribution—the radiative correction —arises from the interaction of the electron-positron virtual pair emitted and absorbed by the real electron. A theoretical expression in terms of the fine structure constant a is... 

A systematic development of relativistic molecular Hamiltonians and various non-relativistic approximations are presented. Our starting point is the Dirac one-fermion Hamiltonian in the presence of an external electromagnetic field. The problems associated with generalizing Dirac s one-fermion theory smoothly to more than one fermion are discussed. The description of many-fermion systems within the framework of quantum electrodynamics (QED) will lead to Hamiltonians which do not suffer from the problems associated with the direct extension of Dirac s one-fermion theory to many-fermion system. An exhaustive discussion of the recent QED developments in the relevant area is not presented, except for cursory remarks for completeness. The non-relativistic form (NRF) of the many-electron relativistic Hamiltonian is developed as the working Hamiltonian. It is used to extract operators for the observables, which represent the response of a molecule to an external electromagnetic radiation field. In this study, our focus is mainly on the operators which eventually were used to calculate the nuclear magnetic resonance (NMR) chemical shifts and indirect nuclear spin-spin coupling constants. 

Another example of zero-point energy arises in the detailed quantum theory of the electromagnetic field, known as quantum electrodynamics. The empty vacuum with no photons present is actually the zero-point level with n = 0. The non-zero energy of this state cannot be measured directly, but does have some observable consequences. The vacuum is really a state of fluctuating electric and magnetic fields that are significant at the atomic level. Without them, there would be no mechanism for the spontaneous emission of photons from excited states. There also have very small effects on the energy levels of atoms (see Section 4.4). 

Abstract. Muonium is a hydrogen-like system which in many respects may be viewed as an ideal atom. Due to the close confinement of the bound state of the two pointlike leptons it can serve as a test object for Quantum Electrodynamics. The nature of the muon as a heavy copy of the electron can be verified. Furthermore, searches for additional, yet unknown interactions between leptons can be carried out. Recently completed experimental projects cover the ground state hyperfine structure, the ls-2s energy interval, a search for spontaneous conversion of muonium into antimuonium and a test of CPT and Lorentz invariance. Precision experiments allow the extraction of accurate values for the electromagnetic fine structure constant, the muon magnetic moment and the muon mass. Most stringent limits on speculative models beyond the standard theory have been set. 

For the literature prior to 1990, see T. Kinoshita Theory of the anomalous magnetic moment of the electron — Numerical approach, in Quantum Electrodynamics, ed. by T. Kinoshita (World Scientific, Singapore, 1990), pp. 218-321... 

Other electron nuclear interaction terms involving 7ra rather than Ia arise from this treatment. However, these terms have all been dealt with in the previous chapter and we do not repeat them here.) The terms in (4.23) are the same as those obtained previously starting from the Dirac equation. Equation (3.244) will yield both the electron and nuclear Zeeman terms and a Breit equation for two nuclei, reduced to non-relativistic form, would yield the nuclear-nuclear interaction terms. Although many nuclei have spins other than 1/2, and even the proton with spin 1 /2 has an anomalous magnetic moment which does not fit the simple Dirac theory, the approach outlined here is fully endorsed by quantum electrodynamics provided that only terms involving M l are retained (see equation (4.23)). The interested reader is referred to Bethe and Salpeter [11] for further details. In our present application we see that the expressions for both... 

The agreement that exists between the measured value of the electron s magnetic moment and the theoretical value calculated with quantum electrodynamics is noteworthy. QED, the most successful theory in physics, is the standard by which other physical theories are judged. The value of the electron s magnetic moment calculated firom QED rather than Dirac theory is... 

The nature of media effects relates to the fact that, since the microscopic displacement field is the net field to which molecules of the medium are exposed, it corresponds to a fundamental electric field dynamically dressed by interaction with the surroundings. The quantized radiation is in consequence described in terms of dressed photons or polaritons. A full and rigorous theory of dressed optical interactions using noncovariant molecular quantum electrodynamics is now available [25-27], and its application to energy transfer processes has been delineated in detail [10]. In the present context its deployment leads to a modification of the quantum operators for the auxiliary fields d and h, which fully account for the influence of the medium—the fundamental fields of course remain unchanged. Expressions for the local displacement electric and the auxiliary magnetic field operators [27], correct for all microscopic interactions, are then as follows... 

In the preceeding sections we have shown the current status of quantum electrodynamical and related calculations in heavy hydrogenlike systems with its unique strong electric and magnetic fields. From our present experimental knowledge there is no contradiction to the theory of quantum electrodynamics as we use it nowadays. However, an increasing experimental precision may still point to deviations in the theory since in Lamb shift calculations the predictions are still at least one order of magnitude more precise than the best experimental values. On the other hand we... 

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