1. If we are interested to the description of the interaction between high-energy charged particles and e.m. field, the convenient choice of the gauge is the Lorentz gauge. In this approach one defines a 4-vector potential $$A^{\mu }=(\varphi ,\;\mathbf{A})\;$$ A μ = ( φ , A ) where $$\mu =0,1,2,3$$ μ = 0 , 1 , 2 , 3 labels the 4-coordinates. Time and space coordinates are grouped into a 4-vector $$x^{\mu }=(ct,\;\mathbf{r).}$$ x μ = ( c t , r ) . The Lorenz-gauge condition is $$(\partial /\partial x^{\mu })A^{\mu }=0$$ ( ∂ / ∂ x μ ) A μ = 0 . See, for instance, the textbook F. Mandl, G. Shaw, Quantum Field Theory (Wiley, New york, 1988)
2. R. Loudon, The Quantum Theory of Light, Chap. 8, (Clarendon Press, Oxford, 1973)
3. W. Greiner, Theoretical Physics, vol. 3, Relativistic Quantum Mechanics: Wave Equations, Chap. 11, (Springer, Berlin, 1990)
4. C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Processus d’interation entre photons et atomes (Editions du CNRS, Paris, 1988)
5. D.A. Varshalovich, A.N. Moskalev, V.K. Kheronskii, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1980)