2002/04/17 by J. D. Jackson · 8 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Quantum and Classical Electrodynamics #Relativity and Gravitational Theory #hep-ph #math-ph #math.MP #physics.class-ph
paper · pdf · doi:10.1119/1.1491265
published as Am.J.Phys.70:917-928,2002 · pdf file, 30 pages, v-gauge references added, submitted for publication
arxiv created 2002/04/17 · openalex publication_date 2002/08/13 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The main purposes of this paper are (i) to illustrate explicitly by a number of examples the gauge functions χ(x,t) whose spatial and temporal derivatives transform one set of electromagnetic potentials into another equivalent set; and (ii) to show that, whatever propagation or nonpropagation characteristics are exhibited by the potentials in a particular gauge, the electric and magnetic fields are always the same and display the experimentally verified properties of causality and propagation at the speed of light. The example of the transformation from the Lorenz gauge (retarded solutions for both scalar and vector potential) to the Coulomb gauge (instantaneous, action-at-a-distance, scalar potential) is treated in detail. A transparent expression is obtained for the vector potential in the Coulomb gauge, with a finite nonlocality in time replacing the expected spatial nonlocality of the transverse current. A class of gauges (v-gauge) is described in which the scalar potential propagates at an arbitrary speed ν relative to the speed of light. The Lorenz and Coulomb gauges are special cases of the v-gauge. The last examples of gauges and explicit gauge transformation functions are the Hamiltonian or temporal gauge, the nonrelativistic Poincaré or multipolar gauge, and the relativistic Fock–Schwinger gauge.