A short proof that the Coulomb-gauge potentials yield the retarded fields

Heras, José A.

doi:10.1088/0143-0807/32/1/020

Cited by 4 publications

(23 citation statements)

References 10 publications

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“…Eqs. (35)(36)(37)(38) are delay-differential equations due to the retardation of the inter-particle interaction. Their initial conditions are not trivial [58,62,[67][68][69][70].…”

Section: Two Point-particles Without Self-interactionsmentioning

confidence: 99%

“…The equality between them is the message of the first law (in the thermally isolated situation, when no heat is involved) [1][2][3]. The task of identifying two aspects of work will be carried out for the relativistic dynamics (35)(36)(37)(38). To make P ′ a source of EMF whose motion is perturbed weakly, we assume that it is much heavier than P:…”

Section: A Formulation Of the First Lawmentioning

confidence: 99%

“…Note that, as implied by (36), there is only the Lorentz force acting on P ′ . Hence the kinetic energy differece (44) can be also recovered as the (time-integrated) mechanic work done by the Lorentz force acting on P ′ .…”

Section: A Formulation Of the First Lawmentioning

confidence: 99%

“…4 The Maxwell equation div E = 4πρ reads [20]: ∆φ( x, t) + 1 c ∂tdiv A( x, t) = −4πρ( x, t). Upon using (9) we get for timedependent φ C ( x, t) in the Coulomb gauge the "static" equation ∆φ C ( x, t) = −4πρ( x, t) implying that φ C ( x, t) responds instantly to changes in the charge density ρ( x, t) [34][35][36]…”

mentioning

confidence: 99%

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Electromagnetic gauge-freedom and work

Allahverdyan¹,

Babajanyan²

2016

J. Phys. A: Math. Theor.

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We argue that the definition of the thermodynamic work done on a charged particle by a timedependent electromagnetic field is an open problem, because the particle's Hamiltonian is not gaugeinvariant. The solution of this problem demands accounting for the source of the field. Hence we focus on the work done by a heavy body (source) on a lighter particle when the interaction between them is electromagnetic and relativistic. The work can be defined via the gauge-invariant kinetic energy of the source. We uncover a formulation of the first law (or the generalized work-energy theorem) which is derived from relativistic dynamics, has definite validity conditions, and relates the work to the particle's Hamiltonian in the Lorenz gauge. Thereby the thermodynamic work also relates to the mechanic work done by the Lorentz force acting on the source. The formulation of the first law is based on a specific separation of the overall energy into those of the source, particle and electromagnetic field. This separation is deduced from a consistent energy-momentum tensor. Hence it holds relativistic covariance and causality.

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“…Eqs. (35)(36)(37)(38) are delay-differential equations due to the retardation of the inter-particle interaction. Their initial conditions are not trivial [58,62,[67][68][69][70].…”

Section: Two Point-particles Without Self-interactionsmentioning

confidence: 99%

Section: A Formulation Of the First Lawmentioning

confidence: 99%

Section: A Formulation Of the First Lawmentioning

confidence: 99%

mentioning

confidence: 99%

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Electromagnetic gauge-freedom and work

Allahverdyan¹,

Babajanyan²

2016

J. Phys. A: Math. Theor.

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“…24,25 When dealing with slowly moving (i.e., non-relativistic) particles in bound states, it is most useful to employ the Coulomb gauge when describing electromagnetic fields, 25,26 and in this case the irrotational parts of the electric and magnetic fields disappear field. (Indeed, the non-zero curls of these fields can be used as an alternative basis for representing electromagnetic properties.)…”

Section: The Nature Of the Mediating Photon In Eetmentioning

confidence: 99%

On the nature of long range electronic coupling in a medium: Distance and orientational dependence for chromophores in molecular aggregates

Lock

Andrews

Jones

2014

The Journal of Chemical Physics

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The electronic coupling that mediates energy transfer in molecular aggregates is theoretically investigated using the principles of quantum electrodynamics (QED). In this context, both the electromagnetic tensor and rate equation relating to these couplings are re-examined with a focus on the role of the relative distance and orientation of transition dipole moment pairs, considering near-, intermediate-, and far-zone contributions to the coupling. The QED based coupling terms are investigated both analytically and numerically, and they are physically interpreted in terms of the character of the mediating (virtual) photons. The spatial dependence of the couplings for a two-dimensional molecular aggregate of ordered and isotropic transition dipole moments is numerically calculated. Further, Pauli Master Equations are employed for a one-dimensional chain of molecules and donor-acceptor pairs, to investigate the importance of intermediate-and far-zone contributions to the electronic coupling on electronic energy transfer dynamics. The results indicate that although Förster theory is often qualitatively and quantitatively correct for describing electronic energy transfer (EET) processes, intermediate-and far-zone coupling terms could sometimes be non-negligible for correctly describing EET in natural and artificial, mesoscopic, solar energy harvesting systems. In particular, the results indicate that these terms are nonnegligible when using Förster resonance energy transfer spectroscopic ruler techniques for distances >10 nm.

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Gauging Potentials: Maxwell, Lorenz, Lorentz and Others on Linking the Electric Scalar and Vector Potentials

Buchwald

2023

Archimedes

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A short proof that the Coulomb-gauge potentials yield the retarded fields

Abstract: A short demonstration that the potentials in the Coulomb gauge yield the retarded electric and magnetic fields is presented. This demonstration is relatively simple and can be presented in an advanced undergraduate curse of electromagnetic theory,

Cited by 4 publications

References 10 publications

Electromagnetic gauge-freedom and work

Electromagnetic gauge-freedom and work

On the nature of long range electronic coupling in a medium: Distance and orientational dependence for chromophores in molecular aggregates

Gauging Potentials: Maxwell, Lorenz, Lorentz and Others on Linking the Electric Scalar and Vector Potentials

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