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Electromagnetic Interaction in the Presence of Isotopic Field-Charges and a Kinetic Field

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Abstract

This paper is a continuation of the article “The Isotopic Field-Charge Assumption Applied to the Electromagnetic Interaction”. It continues the discussion and consequences of the extended Dirac equation in the presence of isotopic mass and electric charges, and a kinetic gauge field. In compliance with the author’s previous papers (Darvas in Concepts Phys. VI(1):3–16, 2009; Int. J. Theor. Phys. 50(10):2961–2991, 2011; Int. J. Theor. Phys., 2013), there appears a second conserved Noether current in the interaction between two electric charges in the presence of isotopic electric charges and a kinetic field. This second conserved current involves the conservation of the isotopic electric charge spin, and that predicts the existence of quanta of the kinetic field (dions associated with the photons). It is concluded that with the discussed conditions, the electromagnetic interaction should be mediated by photons and their dion partners together. The conclusions give physical meaning, among others, to the electric moment and to a virtual coupling spin.

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Notes

  1. While the Dirac equation—introduced and discussed first in his 1928 and 1929 papers [18, 19]—is presented in almost all usual textbooks on QED and field theory, his extension published in 1962 is mentioned rarely (cf., [39]).

  2. Fabbri [22] studies also the metric of Dirac’s field theory with kinematic conditions, in a similar, but also a little bit different context.

  3. Rao and Sireesha [30] noticed that there is not the presence of a scalar field which affects the geometry of the space-time, although it changes the matter distribution.

  4. Similar attempts (like our in the velocity space) were made by [28] in the phase space (with a particular mapping from the configuration space to phase space), and they anticipated the quantization of the models.

  5. Concerning the parallel presence of a scalar and a kinetic gauge field, authors of [31] enlarge the configuration space by including a scalar field additionally, and taking anisotropic models into account too. They also investigated whether Noether’s symmetry holds in the known form alone or doesn’t, that means, whether the single Noether current should be extended (let us add: with another current).

  6. Note, that the potential (Coulomb) charges behave like corpuscles, while the kinetic (Lorentz type) charges like waves [12]. This complementary double behaviour (formulated first by Bohr in 1927, then discussed in 1937 [4]) became subject of studies again (cf., [29]).

  7. Jackiw and Rebbi [23] (with assistance by t’Hooft)—investigating the YM pseudoparticle solution by [3], which was found to be O(5) invariant, and after having applied the solution to the Dirac equation—foresaw and demonstrated that the pseudoparticle was distinguished by possessing a large kinematical invariance group “possibly important in future developments of the theory”, although they did not analyse these kinetic consequences in particular for the Dirac equation.

  8. We called this hypothetical boson “dion”, after the Greek term meaning ‘flee’, ‘flight’, ‘rout’ in English. The name dion brings about some associations of the dyons, which were proposed first by Schwinger, 1969 [32]. Dyon was presumed as a hypothetical particle endowed with both electric and magnetic charges. From our aspect it can be considered as the first idea of doubling the properties of a charged physical object. Although that doubling of properties differed from our distinction between isotopic electric charges that had there a similar feature: it distinguished the Coulomb-like charges from magnetic charges, which were assumed as results of the velocity of current-like (kinetic) charges. Schwinger introduced this concept when he extended the quantization condition, set up earlier by Dirac, to the dyon. By the dyon model, Schwinger predicted a particle with the properties of the J/ψ meson, years before it was discovered in 1974. A sign of the actuality of the topic is a renaissance of the discussion of dyons in the literature of non-Abelian theories [33] and [5]. The latter refers to octonion electrodynamics, what is widely used in the literature, and what we reduced to quaternions in [8]. (Concerning earlier treatments, cf. e.g., [24, 34].)

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    György Darvas

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Darvas, G. Electromagnetic Interaction in the Presence of Isotopic Field-Charges and a Kinetic Field. Int J Theor Phys 53, 39–51 (2014). https://doi.org/10.1007/s10773-013-1781-2

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