On the Emergence of the Coulomb Forces in Quantum Electrodynamics

Naudts, Jan

doi:10.1155/2017/7232798

Cited by 3 publications

(6 citation statements)

References 14 publications

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“…The vectors u (1) , u (2) , v (3) , v (4) are the analogues of the polarization vectors of the photon. They are partly fixed by the requirement that the vector with components ψr satisfies Dirac's equation…”

Section: E3 Dirac's Equationmentioning

confidence: 99%

“…And it is difficult to reconcile them with the aversion of physicists to action at a distance. It is therefore obvious to claim that also the Coulomb forces are emergent forces [3]. While the claim of Verlinde is made in the context of cosmology the emergence of the Coulomb forces is formulated here in the context of quantum field theory.…”

Section: Introductionmentioning

confidence: 99%

“…A theory of Quantum Electrodynamics which does not include Coulomb forces is appealing because it can avoid some of the technical problems which plague the standard version of the theory. The claim made in [3] is that Coulomb attraction and repulsion are carried by transversely polarized photons. This eliminates the need for longitudinal and scalar photons and allows for building a rigorous theory of QED.…”

Section: Introductionmentioning

confidence: 99%

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Emergent Coulomb Forces in Reducible Quantum Electrodynamics

Naudts

2019

Found Sci

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This paper discusses an attempt to develop a mathematically rigorous theory of Quantum Electrodynamics (QED). It deviates from the standard version of QED mainly in two aspects: it is assumed that the Coulomb forces are carried by transversely polarized photons, and a reducible representation of the canonical commutation and anti-commutation relations is used. Both interventions together should suffice to eliminate the mathematical inconsistencies of standard QED.

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Section: E3 Dirac's Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Emergent Coulomb Forces in Reducible Quantum Electrodynamics

Naudts

2019

Found Sci

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“…See [6,7,8,9] and references given there. The present author introduced a simplified formalism [10,11,12]. By starting from gauge transformations, as is done here, the possibility of a rigorously formulated QED can be investigated in a more systematic manner.…”

Section: Introductionmentioning

confidence: 99%

Gauge transformations of a relativistic field of quantum harmonic oscillators

Naudts¹

2020

Preprint

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A set of gauge transformations of a relativistic field of quantum harmonic oscillators is studied in a mathematically rigorous manner. Each wave function in the domain of the number operator of a single oscillator generates a Fréchet-differentiable field of wave functions. Starting from a coherent wave function one obtains a two-dimensional differentiable manifold of coherent vector states. As an illustration it is shown that the gauge transformation can be chosen in such a way that the resulting fields describe a freely-propagating wave.

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“…In fact, it emphasizes the role of these superpositions by assuming that the frequency of the oscillators, and hence the momentum of the photons, is undergoing quantum fluctuations. Recently [20,21], the present author restored the historical assumption of the frequency being a parameter and added some simplifying assumptions to the Czachor formalism. The resulting theory is a reducible version of QED.…”

Section: Introductionmentioning

confidence: 99%

Non-classical correlations in reducible quantum electrodynamics

Naudts

2019

J. Phys. Commun.

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The question is discussed whether the momentum of a photon has a quantum uncertainty or whether it is a classical quantity. The latter assumption is the main characteristic of reducible Quantum Electrodynamics (QED). Recent experiments in Quantum Optics may resolve the question. The non-classical correlation of quantum noise in color-entangled beams cannot be explained by reducible QED without modification of the standing explanation. On the other hand, reducible QED explains uncertainty of the momentum of a single photon when it is entangled with a quantum spin residing in its environment. The explanation of the historical experiment with equally-polarized pairs of photons, showing violation of the Bell inequalities, invokes the argument of collapse of the wave function, also in reducible QED. k k H y = ñ ¢ ¢ | †. The present paper questions whether states of the form (1) or (2) do occur in Nature. If they don't then a modified theory of QED, such as reducible QED, is needed.The original picture behind QED is that Euclidean space is filled with two-dimensional quantum harmonic oscillators the excitations of which are photons. Marek Czachor suggested [11] that the frequency of these oscillators should be quantized as well. Together with his collaborators he developed a non-canonical theory of QED. See [11][12][13][14][15][16][17][18] and references quoted in these papers. One of the main results of the theory is that QED after renormalization is recovered as a limiting case, without the need to fall back on ad hoc procedures like renormalization. On the other hand, an attempt to force the formalism into a mathematically rigorous framework was not successful [19].

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On the Emergence of the Coulomb Forces in Quantum Electrodynamics

Cited by 3 publications

References 14 publications

Emergent Coulomb Forces in Reducible Quantum Electrodynamics

Emergent Coulomb Forces in Reducible Quantum Electrodynamics

Gauge transformations of a relativistic field of quantum harmonic oscillators

Non-classical correlations in reducible quantum electrodynamics

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