Quantum electrodynamics potential

QUANTUM ELECTRODYNAMICS POTENTIALS, GAUGE INVARIANCE, AND ANALOGY TO CLASSICAL ELECTRODYNAMICS... 

This section has outlined the current formulations of quantum electrodynamics. Since the theory assumes its local form when expressed in terms of potentials, these formulations were in terms of the... 

Crowell discovered a variety of effects numerically, including modified Rabi flopping, which has an inverse frequency dependence similar to that observed in the solid state in reciprocal noise [73]. The latter is also explained by Crowell [17] using a non-Abelian model. A variety of other effects of RFR on the quantum electrodynamical level was also reported numerically [17]. The overall result is that the occurrence, classically, of the B V> field means that there is a quantum electrodynamical Hamiltonian generated by the classical term proportional to 3 2. This induces transitional behavior because it contributes to the dynamics of probability amplitudes [17]. The Hamiltonian is a quartic potential where the value of determines the value of the potential. The latter has two minima one where B = 0 and the other for a finite value of the B i) field, corresponding to states that are invariants of the Lagrangian but not of the vacuum. 

In quantum electrodynamics (QED) the potentials asume a more important role in the formulation, as they are related to a phase shift in the wavefunction. This is still an integral effect over the path of interest. This manifests itself in the phase shift of an electron around a closed path enclosing a magnetic field, even though there are no fields (approximately) on the path itself (static conditions). As can be shown the result of such an experiment is gauge-invariant, allowing the use of various choices of the vector potential (all giving the same result). 

In formulating quantum electrodynamics (QED), it has been found convenient to introduce the electromagnetic interaction with charged particles via the potentials instead of the fields. Consider a particle of charge q traveling on some path P from i to 2. Then the magnetic change in phase of the wavefunction is just... 

E. Baum, Vector and Scalar Potentials away from Sources, and Gauge Invariance in Quantum Electrodynamics, Physics Note 3 (1991). 

What has been presented here is a semiclassical theory of TJ 1) quantum electrodynamics. Here the electromagnetic field is treated in a purely classical manner, but where the electromagnetic potential has been normalized to include one photon per some unit volume. Here the absorption and emission of a photon is treated in a purely perturbative manner. Further, the field normalization is done so that each unit volume contains the equivalent of n photons and that the energy is computed accordingly. However, this is not a complete theory, for it is known that the transition probability is proportional to n + 1. So the semiclassical theory is only appropriate when the number of photons is comparatively large. 

It is apparent that for A3, = 0, the electric field component does not contain a product of potential terms. In general the vanishing of this term occurs if there are no longitudinal electric field components. Within the framework of most quantum electrodynamic, or quantum optical, calculations this is often the case. The B(3) field then is a Fourier sum over modes with operators a qaq. The B(3 ) field is then directed orthogonal to the plane defined by A1 and A2. The fourdimensional dual to this term is defined on a time-like surface that has the interpretation, under dyad-vector duality in three dimensions as, as an electric... 

A negative imaginary potential in the time-independent Schrodinger equation absorbs the particle flux, thus violating the law of conservation of flux, which is satisfied for real potentials [12,13]. Then, the quantum electrodynamical phenomenon of pair annihilation can be represented by particle loss due to an effective absorption potential H = —zVabs since the exact mechanism of positron loss is totally irrelevant to the study of the atomic processes in consideration [9,10,14-16]. The only important aspect of pair annihilation for the present purpose is the correct description of the loss rate. The absorption potential H is proportional to the delta function 5 (r) of the e+-e distance vector r (Section 4.2). 

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