Lorentz gauge condition

This vector potential si should not be confused with the vector potential for the radiation field introduced in Section 9.8 of Chapter 9. The vector potential si of the present section obeys the equation Qsi = ji. We have denoted it by script cap si to indicate that it satisfies the transversality condition div si as 0 in contradistinction to the Lorentz gauge potentials A to be introduced later, which satisfy d A x) as 0 and QAp =... 

Asymptotic Condition.—In Section 11.1, we exhibited the equivalence of the formulation of quantum electrodynamics in the Coulomb and Lorentz gauges in so far as observable quantities were concerned (t.e., scattering amplitudes). We also noted that both of these formulations, when based on a hamiltonian not containing mass renormalization counter terms, suffered from the difficulty that the... 

In the present section we shall make this difficulfy apparent in a somewhat different way by showing that it is not possible to satisfy the asymptotic condition when the theory is formulated in terms of an unsubtracted hamiltonian of the form jltAll(x) — JS0JV. We shall work in the Lorentz gauge, where the relativistic invariance of the theory is more obvious. 

Lorentz approximation, 46 Lorentz condition, 551 Lorentz gauge, 657,664 Lorentz group homogeneous, 490... 

Incidentally, the Lorenz gauge was proposed by the Danish physicist Ludvig Lorenz, It is often erroneously designated Lorentz gauge, after the more famous Dutch physicist Hendrik Lorentz. In fact, the condition does fulfill the property known as Lorentz invariance.)... 

This condition is called the Lorentz condition and defines the Lorentz gauge. Using this condition in (3.19) provides us finally with a set of decoupled equations ... 

As in the spin 0 and spin case we could next introduce creation and anniliilation operators. This is most conveniently done by working with the representatives that satisfy in a given Lorentz frame the three dimensional transversality condition, i.e., by working in the radiation gauge. We shall, however, adopt a slightly different procedure, which is outlined in the next section. 

Quantization of radiation field in terms of field intensity operators, 562 Quantum electrodynamics, 642 asymptotic condition, 698 gauge invariance in relation to operators inducing inhomogeneous Lorentz transformations, 678 invariance properties, 664 invariance under discrete transformations, 679... 

---