Gauge quantum electrodynamics

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... 

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... 

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

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). 

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

The electromagnetic helicity has also been studied by Evans [54—57], especially its consequences for his new non-Abelian SO(3) gauge version of QED (quantum electrodynamics). 

E. A. Power, S. Zienau, Coulomb Gauge in Non-Relativistic Quantum Electrodynamics and the Shape of Spectral Lines. Phil. Trans. Roy. Soc. Lond. A 251 (1959) 427. 

We have recently studied the question of gauge invariance in non-relativistic quantum electrodynamics in a general setting [5]. The principal results... 

---